Question

Solve$(b-3{)}^2-8=24$.

Short answer

The solutions are$b=3\pm 4\sqrt{2}$.

Step-by-step solution

Given Information.   

The Given equation is$(b-3{)}^2-8=24$.

Isolate the binomial term. 

$$\begin{gathered} (b-3{)}^2=24+8 \\ (b-3{)}^2=32 \end{gathered}$$

Use the square root property. 

$b-3=\pm \sqrt{32}$

Factor the radical.

$$\begin{gathered} b-3=\pm \sqrt{2\times 2\times 2\times 2\times 2} \\ b-3=\pm 4\sqrt{2} \end{gathered}$$

Solve for b.

$b=3\pm 4\sqrt{2}$

Rewrite to show two solutions.

$$\begin{gathered} b=3+4\sqrt{2}, \\ b=3-4\sqrt{2} \end{gathered}$$