Question

solve this equation for x:
\sqrt{3x + 7} - x = 3.
select the correct answer.
\bigcirc x = 1, 2
\bigcirc x = -2, -1
\bigcirc x = 2, 8
\bigcirc x = -8, -2

Explanation:

Step1: Isolate the square root

$\sqrt{3x + 7} = x + 3$

Step2: Square both sides

$(\sqrt{3x + 7})^2 = (x + 3)^2$
$3x + 7 = x^2 + 6x + 9$

Step3: Rearrange to quadratic form

$x^2 + 3x + 2 = 0$

Step4: Factor the quadratic

$(x + 1)(x + 2) = 0$

Step5: Solve for x, check validity

Test $x=-1$: $\sqrt{3(-1)+7} - (-1) = \sqrt{4} +1=2+1=3$ (valid)
Test $x=-2$: $\sqrt{3(-2)+7} - (-2) = \sqrt{1} +2=1+2=3$ (valid)

Answer:

B. $x = -2, -1$