Question

solve for $b$. $4b^2 - 9 = 87$
$b = 4\sqrt{6}, b = -4\sqrt{6}$
$b = 4, b = -4$
$b = 2\sqrt{2}, b = -2\sqrt{2}$
$b = 2\sqrt{6}, b = -2\sqrt{6}$

Explanation:

Step1: Isolate the squared term

Add 9 to both sides:
$4b^2 = 87 + 9$
$4b^2 = 96$

Step2: Solve for $b^2$

Divide both sides by 4:
$b^2 = \frac{96}{4}$
$b^2 = 24$

Step3: Solve for $b$

Take square root of both sides:
$b = \pm\sqrt{24}$
Simplify $\sqrt{24} = \sqrt{4\times6} = 2\sqrt{6}$, so
$b = 2\sqrt{6}, b = -2\sqrt{6}$

Answer:

$b = 2\sqrt{6}, b = -2\sqrt{6}$