Question

question 6 of 10
which of the following are solutions to the equation below?
check all that apply.
x² + 6x + 9 = 20
a. x = -2√5 + 3
b. x = 2√5 + 3
c. x = -2√5 - 3
d. x = 2√5 - 3
e. x = √3 + 20
f. x = -√3 + 20

Explanation:

Step1: Recognize perfect - square trinomial

The left - hand side of the equation $x^{2}+6x + 9$ is a perfect - square trinomial, which can be factored as $(x + 3)^{2}$. So the equation becomes $(x + 3)^{2}=20$.

Step2: Take square root of both sides

Taking the square root of both sides, we get $x+3=\pm\sqrt{20}=\pm2\sqrt{5}$.

Step3: Solve for x

Subtract 3 from both sides of the equation. When $x + 3=2\sqrt{5}$, $x=2\sqrt{5}-3$; when $x + 3=-2\sqrt{5}$, $x=-2\sqrt{5}-3$.

Answer:

C. $x=-2\sqrt{5}-3$, D. $x=2\sqrt{5}-3$