Question

When solving a problem that uses the completing the square method, after you complete the square, what would the perfect square trinomial be for the problem:

2x^2+12x=32
options::
A) (x+3)^2 = 25
B) (x+3)^2 = 41
C) (x+6)^2 = 68
D) (x+6)^2 = 25

Answer 1

Answer: A

Explanation:

First, let's rewrite the given equation to have the constant term on the right side:

2x^2 + 12x = 32

2x^2 + 12x - 32 = 0

To use the completing the square method, we need to make the coefficient of the x^2 term equal to 1. We can do this by dividing the entire equation by 2:

x^2 + 6x - 16 = 0

Now, we will complete the square for the quadratic expression on the left side. To do this, we take half of the coefficient of the x term (6/2 = 3) and square it (3^2 = 9). Then, we add and subtract this value inside the parenthesis:

x^2 + 6x + 9 - 9 - 16 = 0

Now, the left side of the equation has a perfect square trinomial:

(x^2 + 6x + 9) - 25 = 0

The trinomial can be written as a square of a binomial:

(x + 3)^2 - 25 = 0

Now, let's move the constant term to the right side of the equation:

(x + 3)^2 = 25

The perfect square trinomial for the problem is (x + 3)^2 = 25