Question

solve the equation by the square root property. 2(x + 9)² = 24 the solution set is (type an exact answer, using radicals as needed. use a comma to separate answers as needed. simplify your answer.)

Explanation:

Step1: Isolate the squared term

Divide both sides by 2.
$\frac{2(x+9)^2}{2} = \frac{24}{2}$
$(x+9)^2 = 12$

Step2: Apply square root property

Take square roots of both sides.
$x+9 = \pm\sqrt{12}$

Step3: Simplify the radical

Simplify $\sqrt{12}$ to $2\sqrt{3}$.
$x+9 = \pm2\sqrt{3}$

Step4: Solve for x

Subtract 9 from both sides.
$x = -9 \pm 2\sqrt{3}$

Answer:

$\boldsymbol{-9 + 2\sqrt{3}, -9 - 2\sqrt{3}}$