Question

What equation results from completing the square and then factoring?

x2 + 4x = 7
a. (x+2)^2 = 11
b. (x + 4)^2 = 11
c. (x + 2)^2 = 3
d. (x + 4)^2 = 3

Answer 1

The correct equation after completing the square and factoring is (x + 2)^2 = 11. This is done by adding the square of half the x coefficient to both sides of the equation and then simplifying.

Step-by-step explanation:

To determine which equation results from completing the square and then factoring, we start with the original equation x2 + 4x = 7. First, we make one side of the equation a perfect square trinomial. We can do this by adding the square of half the coefficient of x, which in this case is 2, to both sides of the equation:

x2 + 4x + (4/2)2 = 7 + (4/2)2

x2 + 4x + 4 = 7 + 4

This simplifies to:

(x + 2)2 = 11

After completing the square, we have factored the left side as a square of a binomial. Therefore, the equation that results from completing the square and then factoring is (x + 2)2 = 11, which corresponds to answer choice (a).