Question

What equation results from completing the square and then factoring?

x^2 + 4x = 15

a)4
b)16
c)8
d)2

Answer 1

Completing the square for the equation x^2 + 4x = 15 involves forming a perfect square trinomial, resulting in (x + 2)^2 = 19 once completed and simplified.

Step-by-step explanation:

The equation resulting from completing the square and then factoring is not explicitly provided in the question body, yet the student seems to be asking about the process using an equation like x^2 + 4x = 15. To complete the square, we need to form a perfect square trinomial on the left side. Here's how you can do that:

• Add and subtract (b/2)^2 to the left side, where b is the coefficient of x. For x^2 + 4x, we have (4/2)^2 = 4.
• Modify the equation: x^2 + 4x + 4 - 4 = 15.
• Rewrite it as: (x + 2)^2 - 4 = 15.
• To find the value when factored, add 4 to both sides resulting in (x + 2)^2 = 19.

Note that the options given a)4 b)16 c)8 d)2 do not apply to the completed and factored form of the given equation. These options may represent a misunderstanding of the process or a separate part of the same problem not included in the question.