Ashford University Algebra Discussion

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Mathematics

ashford university

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A SAMPLE IS ATTACHED BUT THE SAMPLE QUESTIONS ARE BASED ON DIFFERENT NUMBERS OF COURSE

Use FACTORING to solve:

x2 + 3x – 18 = 0

Use the QUADRATIC FORMULA to solve:

(a - 2) ^ 2 = 8

For the factoring problem, be sure you show all steps to the  factoring and solving. Show a check of your solutions back into the  original equation.

For the quadratic formula problem, be sure that you use readable  notation while you are working the computational steps. Refer to the  Inserting Math Symbols handout for guidance with formatting.

Present your final solutions as decimal approximations carried out  to the third decimal place. Due to the nature of these solutions, no  check is required.

Incorporate the following four math vocabulary words into your discussion. Use bold  font to emphasize the words in your writing. Do not write definitions  for the words; use them appropriately in sentences describing your math  work.

Quadratic formula

Factoring

Completing the square

Discriminant

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For our week 4 discussion post we were asked to solve two separate equations using Factoring and the Quadratic Formula respectively. The first equation for my number 8 that needs to be solved is 22 - 2x - 24 = 0 and we will be using factoring to do so. Factoring 22 - 2x - 24 = 0 using the AC method. Consider the form 2? + bc +c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -24 and whose sum is -2. -6,4 Write the factored form using these integers. (x-6) (x + 4) = 0 Set x-6 equal to 0 and solve for x. Set the factor equal to 0.x+4=0 Subtract 4 from both sides of the equation. 2-4 Unread The second equation is (x + 5)2 = 4 and we will solve this equation using the quadratic formula. The first we do is move the 4 to the left side of the equation by subtracting it from both sides. (x + 5)2 - 4= 0 Use the quadratic formula to find the solutions. -6312-4(ac) 20 Substitute the values a=1, b=10, and c=21 into the quadratic formula and solve for x. -104/102-4(1-21) 2.1 Simplify the numerator - 10:14 Multiply 2 by 1.c = -1004 Simplify - -104 = -5 + 2 The final answer is the combination of both solutions. x= -3,-7
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Explanation & Answer

Attached is the solution.

1. Use Factoring to solve: 𝑥 2 + 3𝑥 – 18 = 0
Let us compare the quadratic equation with the standard form:
𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
We have,
a = 1, b = 3 and c = −18
Using the factorization method, we identify factors of the quadratic equation. For a
quadratic equation, the number of factors are two henceforth, we try to find a pair of
integers such that their product equals 𝑎 ∗ 𝑐 and when their summation equal b.
In the given problem, the product of the two integers should be 𝑎 ∗ 𝑐 = 1 ∗ (−1...


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