Question

solve the equation by the square root property.
3(x + 1)² = 54
the solution set is
(type an exact answer, using radicals as needed. use a comma to separate answers as needed. simplify

Explanation:

Step1: Isolate the squared term

Divide both sides by 3:
$\frac{3(x+1)^2}{3} = \frac{54}{3}$
Simplify to get:
$(x+1)^2 = 18$

Step2: Apply square root property

Take square roots of both sides:
$x+1 = \pm\sqrt{18}$
Simplify $\sqrt{18}$ to $3\sqrt{2}$:
$x+1 = \pm3\sqrt{2}$

Step3: Solve for x

Subtract 1 from both sides:
$x = -1 \pm 3\sqrt{2}$

Answer:

$\boldsymbol{-1 + 3\sqrt{2}, -1 - 3\sqrt{2}}$