Algebra 2 - Using Quadratic Formula/ a-c for each quadratic equation

Algebra
Tutor: None Selected Time limit: 1 Day

These are homework questions that I have, and need help to solve them.

1. 4x^2 - 9 = -7x - 4

2. 12x^2 + 9x - 2 = -17

3. 2x^2 + 3x - 3 = 0

4. 6x^2 + 5x - 1 = 0

5. 3x^2 - 3x + 8 = 0

6. -5x^2 + 4x + 1 = 0

7. -3x^2 - 7x + 2 = 6

8. x^2 + 2x - 4 = -9

May 8th, 2015

  1. Simplifying
    12x2 + 9x + 15 = 0
    
    Reorder the terms:
    15 + 9x + 12x2 = 0
    
    Solving
    15 + 9x + 12x2 = 0
    
    Solving for variable 'x'.
    
    Factor out the Greatest Common Factor (GCF), '3'.
    3(5 + 3x + 4x2) = 0
    
    Ignore the factor 3.
    

    Subproblem 1

    Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75x + x2 = 0 + -1.25 0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75x + x2 = -1.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

  2. 2.
    
    Simplifying
    12x2 + 9x + -2 = -17
    
    Reorder the terms:
    -2 + 9x + 12x2 = -17
    
    Solving
    -2 + 9x + 12x2 = -17
    
    Solving for variable 'x'.
    
    Reorder the terms:
    -2 + 17 + 9x + 12x2 = -17 + 17
    
    Combine like terms: -2 + 17 = 15
    15 + 9x + 12x2 = -17 + 17
    
    Combine like terms: -17 + 17 = 0
    15 + 9x + 12x2 = 0
    
    Factor out the Greatest Common Factor (GCF), '3'.
    3(5 + 3x + 4x2) = 0
    
    Ignore the factor 3.
    

    Subproblem 1

    Set the factor '(5 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 4x2 = 0 Solving 5 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 0.75x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 0.75x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 0.75x + x2 = 0 + -1.25 0.75x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 0.75x + x2 = -1.25 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -1.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -1.25 + 0.140625 Combine like terms: -1.25 + 0.140625 = -1.109375 0.140625 + 0.75x + x2 = -1.109375 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -1.109375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
    3.
    Simplifying
    2x2 + 3x + -3 = 0
    
    Reorder the terms:
    -3 + 3x + 2x2 = 0
    
    Solving
    -3 + 3x + 2x2 = 0
    
    Solving for variable 'x'.
    
    Begin completing the square.  Divide all terms by
    2 the coefficient of the squared term: 
    
    Divide each side by '2'.
    -1.5 + 1.5x + x2 = 0
    
    Move the constant term to the right:
    
    Add '1.5' to each side of the equation.
    -1.5 + 1.5x + 1.5 + x2 = 0 + 1.5
    
    Reorder the terms:
    -1.5 + 1.5 + 1.5x + x2 = 0 + 1.5
    
    Combine like terms: -1.5 + 1.5 = 0.0
    0.0 + 1.5x + x2 = 0 + 1.5
    1.5x + x2 = 0 + 1.5
    
    Combine like terms: 0 + 1.5 = 1.5
    1.5x + x2 = 1.5
    
    The x term is 1.5x.  Take half its coefficient (0.75).
    Square it (0.5625) and add it to both sides.
    
    Add '0.5625' to each side of the equation.
    1.5x + 0.5625 + x2 = 1.5 + 0.5625
    
    Reorder the terms:
    0.5625 + 1.5x + x2 = 1.5 + 0.5625
    
    Combine like terms: 1.5 + 0.5625 = 2.0625
    0.5625 + 1.5x + x2 = 2.0625
    
    Factor a perfect square on the left side:
    (x + 0.75)(x + 0.75) = 2.0625
    
    Calculate the square root of the right side: 1.436140662
    
    Break this problem into two subproblems by setting 
    (x + 0.75) equal to 1.436140662 and -1.436140662.
    
    

    Subproblem 1

    x + 0.75 = 1.436140662 Simplifying x + 0.75 = 1.436140662 Reorder the terms: 0.75 + x = 1.436140662 Solving 0.75 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.436140662 + -0.75 x = 1.436140662 + -0.75 Combine like terms: 1.436140662 + -0.75 = 0.686140662 x = 0.686140662 Simplifying x = 0.686140662

    Subproblem 2

    x + 0.75 = -1.436140662 Simplifying x + 0.75 = -1.436140662 Reorder the terms: 0.75 + x = -1.436140662 Solving 0.75 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.436140662 + -0.75 x = -1.436140662 + -0.75 Combine like terms: -1.436140662 + -0.75 = -2.186140662 x = -2.186140662 Simplifying x = -2.186140662

    Solution

    The solution to the problem is based on the solutions from the subproblems. x = {0.686140662, -2.186140662}
  3. 4.
    Simplifying
    6x2 + 5x + -1 = 0
    
    Reorder the terms:
    -1 + 5x + 6x2 = 0
    
    Solving
    -1 + 5x + 6x2 = 0
    
    Solving for variable 'x'.
    
    Begin completing the square.  Divide all terms by
    6 the coefficient of the squared term: 
    
    Divide each side by '6'.
    -0.1666666667 + 0.8333333333x + x2 = 0
    
    Move the constant term to the right:
    
    Add '0.1666666667' to each side of the equation.
    -0.1666666667 + 0.8333333333x + 0.1666666667 + x2 = 0 + 0.1666666667
    
    Reorder the terms:
    -0.1666666667 + 0.1666666667 + 0.8333333333x + x2 = 0 + 0.1666666667
    
    Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
    0.0000000000 + 0.8333333333x + x2 = 0 + 0.1666666667
    0.8333333333x + x2 = 0 + 0.1666666667
    
    Combine like terms: 0 + 0.1666666667 = 0.1666666667
    0.8333333333x + x2 = 0.1666666667
    
    The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
    Square it (0.1736111111) and add it to both sides.
    
    Add '0.1736111111' to each side of the equation.
    0.8333333333x + 0.1736111111 + x2 = 0.1666666667 + 0.1736111111
    
    Reorder the terms:
    0.1736111111 + 0.8333333333x + x2 = 0.1666666667 + 0.1736111111
    
    Combine like terms: 0.1666666667 + 0.1736111111 = 0.3402777778
    0.1736111111 + 0.8333333333x + x2 = 0.3402777778
    
    Factor a perfect square on the left side:
    (x + 0.4166666667)(x + 0.4166666667) = 0.3402777778
    
    Calculate the square root of the right side: 0.583333333
    
    Break this problem into two subproblems by setting 
    (x + 0.4166666667) equal to 0.583333333 and -0.583333333.
    
    

    Subproblem 1

    x + 0.4166666667 = 0.583333333 Simplifying x + 0.4166666667 = 0.583333333 Reorder the terms: 0.4166666667 + x = 0.583333333 Solving 0.4166666667 + x = 0.583333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.583333333 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.583333333 + -0.4166666667 x = 0.583333333 + -0.4166666667 Combine like terms: 0.583333333 + -0.4166666667 = 0.1666666663 x = 0.1666666663 Simplifying x = 0.1666666663

    Subproblem 2

    x + 0.4166666667 = -0.583333333 Simplifying x + 0.4166666667 = -0.583333333 Reorder the terms: 0.4166666667 + x = -0.583333333 Solving 0.4166666667 + x = -0.583333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.583333333 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.583333333 + -0.4166666667 x = -0.583333333 + -0.4166666667 Combine like terms: -0.583333333 + -0.4166666667 = -0.9999999997 x = -0.9999999997 Simplifying x = -0.9999999997

    Solution

    The solution to the problem is based on the solutions from the subproblems. x = {0.1666666663, -0.9999999997}
  4. 5.
    Simplifying
    3x2 + -3x + 8 = 0
    
    Reorder the terms:
    8 + -3x + 3x2 = 0
    
    Solving
    8 + -3x + 3x2 = 0
    
    Solving for variable 'x'.
    
    Begin completing the square.  Divide all terms by
    3 the coefficient of the squared term: 
    
    Divide each side by '3'.
    2.666666667 + -1x + x2 = 0
    
    Move the constant term to the right:
    
    Add '-2.666666667' to each side of the equation.
    2.666666667 + -1x + -2.666666667 + x2 = 0 + -2.666666667
    
    Reorder the terms:
    2.666666667 + -2.666666667 + -1x + x2 = 0 + -2.666666667
    
    Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
    0.000000000 + -1x + x2 = 0 + -2.666666667
    -1x + x2 = 0 + -2.666666667
    
    Combine like terms: 0 + -2.666666667 = -2.666666667
    -1x + x2 = -2.666666667
    
    The x term is -1x.  Take half its coefficient (-0.5).
    Square it (0.25) and add it to both sides.
    
    Add '0.25' to each side of the equation.
    -1x + 0.25 + x2 = -2.666666667 + 0.25
    
    Reorder the terms:
    0.25 + -1x + x2 = -2.666666667 + 0.25
    
    Combine like terms: -2.666666667 + 0.25 = -2.416666667
    0.25 + -1x + x2 = -2.416666667
    
    Factor a perfect square on the left side:
    (x + -0.5)(x + -0.5) = -2.416666667
    
    Can't calculate square root of the right side.
    
    The solution to this equation could not be determined.
  5. 6.
    Simplifying
    -5x2 + 4x + 1 = 0
    
    Reorder the terms:
    1 + 4x + -5x2 = 0
    
    Solving
    1 + 4x + -5x2 = 0
    
    Solving for variable 'x'.
    
    Begin completing the square.  Divide all terms by
    -5 the coefficient of the squared term: 
    
    Divide each side by '-5'.
    -0.2 + -0.8x + x2 = 0
    
    Move the constant term to the right:
    
    Add '0.2' to each side of the equation.
    -0.2 + -0.8x + 0.2 + x2 = 0 + 0.2
    
    Reorder the terms:
    -0.2 + 0.2 + -0.8x + x2 = 0 + 0.2
    
    Combine like terms: -0.2 + 0.2 = 0.0
    0.0 + -0.8x + x2 = 0 + 0.2
    -0.8x + x2 = 0 + 0.2
    
    Combine like terms: 0 + 0.2 = 0.2
    -0.8x + x2 = 0.2
    
    The x term is -0.8x.  Take half its coefficient (-0.4).
    Square it (0.16) and add it to both sides.
    
    Add '0.16' to each side of the equation.
    -0.8x + 0.16 + x2 = 0.2 + 0.16
    
    Reorder the terms:
    0.16 + -0.8x + x2 = 0.2 + 0.16
    
    Combine like terms: 0.2 + 0.16 = 0.36
    0.16 + -0.8x + x2 = 0.36
    
    Factor a perfect square on the left side:
    (x + -0.4)(x + -0.4) = 0.36
    
    Calculate the square root of the right side: 0.6
    
    Break this problem into two subproblems by setting 
    (x + -0.4) equal to 0.6 and -0.6.
    
    

    Subproblem 1

    x + -0.4 = 0.6 Simplifying x + -0.4 = 0.6 Reorder the terms: -0.4 + x = 0.6 Solving -0.4 + x = 0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.6 + 0.4 x = 0.6 + 0.4 Combine like terms: 0.6 + 0.4 = 1 x = 1 Simplifying x = 1

    Subproblem 2

    x + -0.4 = -0.6 Simplifying x + -0.4 = -0.6 Reorder the terms: -0.4 + x = -0.6 Solving -0.4 + x = -0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.6 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.6 + 0.4 x = -0.6 + 0.4 Combine like terms: -0.6 + 0.4 = -0.2 x = -0.2 Simplifying x = -0.2

    Solution

    The solution to the problem is based on the solutions from the subproblems. x = {1, -0.2}
  6. 7.
    Simplifying
    -3x2 + -7x + 2 = 6
    
    Reorder the terms:
    2 + -7x + -3x2 = 6
    
    Solving
    2 + -7x + -3x2 = 6
    
    Solving for variable 'x'.
    
    Reorder the terms:
    2 + -6 + -7x + -3x2 = 6 + -6
    
    Combine like terms: 2 + -6 = -4
    -4 + -7x + -3x2 = 6 + -6
    
    Combine like terms: 6 + -6 = 0
    -4 + -7x + -3x2 = 0
    
    Factor out the Greatest Common Factor (GCF), '-1'.
    -1(4 + 7x + 3x2) = 0
    
    Ignore the factor -1.
    

    Subproblem 1

    Set the factor '(4 + 7x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + 3x2 = 0 Solving 4 + 7x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 2.333333333x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 2.333333333x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + -1.333333333 2.333333333x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 2.333333333x + x2 = -1.333333333 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = -1.333333333 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -1.333333333 + 1.361111112 Combine like terms: -1.333333333 + 1.361111112 = 0.027777779 1.361111112 + 2.333333333x + x2 = 0.027777779 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 0.027777779 Calculate the square root of the right side: 0.16666667 Break this problem into two subproblems by setting (x + 1.166666667) equal to 0.16666667 and -0.16666667.

    Subproblem 1

    x + 1.166666667 = 0.16666667 Simplifying x + 1.166666667 = 0.16666667 Reorder the terms: 1.166666667 + x = 0.16666667 Solving 1.166666667 + x = 0.16666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 0.16666667 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.16666667 + -1.166666667 x = 0.16666667 + -1.166666667 Combine like terms: 0.16666667 + -1.166666667 = -0.999999997 x = -0.999999997 Simplifying x = -0.999999997

    Subproblem 2

    x + 1.166666667 = -0.16666667 Simplifying x + 1.166666667 = -0.16666667 Reorder the terms: 1.166666667 + x = -0.16666667 Solving 1.166666667 + x = -0.16666667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -0.16666667 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.16666667 + -1.166666667 x = -0.16666667 + -1.166666667 Combine like terms: -0.16666667 + -1.166666667 = -1.333333337 x = -1.333333337 Simplifying x = -1.333333337

    Solution

    The solution to the problem is based on the solutions from the subproblems. x = {-0.999999997, -1.333333337}

    Solution

    x = {-0.999999997, -1.333333337}
  7. 8.
    Simplifying
    x2 + 2x + -4 = -9
    
    Reorder the terms:
    -4 + 2x + x2 = -9
    
    Solving
    -4 + 2x + x2 = -9
    
    Solving for variable 'x'.
    
    Reorder the terms:
    -4 + 9 + 2x + x2 = -9 + 9
    
    Combine like terms: -4 + 9 = 5
    5 + 2x + x2 = -9 + 9
    
    Combine like terms: -9 + 9 = 0
    5 + 2x + x2 = 0
    
    Begin completing the square.
    
    Move the constant term to the right:
    
    Add '-5' to each side of the equation.
    5 + 2x + -5 + x2 = 0 + -5
    
    Reorder the terms:
    5 + -5 + 2x + x2 = 0 + -5
    
    Combine like terms: 5 + -5 = 0
    0 + 2x + x2 = 0 + -5
    2x + x2 = 0 + -5
    
    Combine like terms: 0 + -5 = -5
    2x + x2 = -5
    
    The x term is 2x.  Take half its coefficient (1).
    Square it (1) and add it to both sides.
    
    Add '1' to each side of the equation.
    2x + 1 + x2 = -5 + 1
    
    Reorder the terms:
    1 + 2x + x2 = -5 + 1
    
    Combine like terms: -5 + 1 = -4
    1 + 2x + x2 = -4
    
    Factor a perfect square on the left side:
    (x + 1)(x + 1) = -4
    
    Can't calculate square root of the right side.
    
    The solution to this equation could not be determined.

May 8th, 2015

Thank you so much! I'll look over them and ask if I don't get a part for each one if I'm able to. But I will later because I have to go out for a little bit.

May 8th, 2015

be assured of my services!.....................................

May 8th, 2015

Will I be able to ask questions if I don't get something?

May 8th, 2015

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