Question

$\frac{3}{2}(x - 2)^2 = 72$

Explanation:

Step1: Eliminate the fraction

Multiply both sides of the equation by $\frac{2}{3}$ to get rid of the coefficient $\frac{3}{2}$ on the left side.
$$(x - 2)^2=72\times\frac{2}{3}$$
$$(x - 2)^2 = 48$$

Step2: Take square roots

Take the square root of both sides. Remember that when taking the square root, we consider both the positive and negative roots.
$$x - 2=\pm\sqrt{48}$$
Simplify $\sqrt{48}$: $\sqrt{48}=\sqrt{16\times3}=4\sqrt{3}$
So we have $x - 2=\pm4\sqrt{3}$

Step3: Solve for x

Add 2 to both sides of the equation to solve for x.
$$x = 2\pm4\sqrt{3}$$

Answer:

$x = 2 + 4\sqrt{3}$ or $x = 2 - 4\sqrt{3}$