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

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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 1Set 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 1Set 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 1x + 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 2x + 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

SolutionThe 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 1x + 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 2x + 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

SolutionThe 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 1x + -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 2x + -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

SolutionThe 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 1Set 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 1x + 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 2x + 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

SolutionThe solution to the problem is based on the solutions
from the subproblems.
x = {-0.999999997, -1.333333337}Solutionx = {-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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May 8th, 2015
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May 8th, 2015
Oct 22nd, 2017
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