Question

Question was provided via image upload.

Explanation:

Step1: Isolate the squared term

Add 5 to both sides of the equation $\frac{1}{4}(x + 2)^2 - 5 = 22$:
$\frac{1}{4}(x + 2)^2 = 22 + 5$
$\frac{1}{4}(x + 2)^2 = 27$

Step2: Eliminate the fraction

Multiply both sides by 4:
$(x + 2)^2 = 27 \times 4$
$(x + 2)^2 = 108$

Step3: Take square roots

Take the square root of both sides:
$x + 2 = \pm\sqrt{108}$
Simplify $\sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3}$:
$x + 2 = \pm 6\sqrt{3}$

Step4: Solve for \( x \)

Subtract 2 from both sides:
$x = -2 \pm 6\sqrt{3}$

Answer:

\( x = -2 + 6\sqrt{3} \) or \( x = -2 - 6\sqrt{3} \) (or approximately \( x \approx 8.392 \) or \( x \approx -12.392 \))