Question

Solve the quadratic equation using square root property.

$(b-1{)}^2-9=39$

Short answer

The solutions are$b=1\pm 4\sqrt{3}$.

Step-by-step solution

Given Information.

The Given equation is$(b-1{)}^2-9=39$.

Isolate the binomial term. 

$$\begin{gathered} (b-1{)}^2=39+9 \\ (b-1{)}^2=48 \end{gathered}$$

Use the square root property. 

$b-1=\sqrt{48}$

Factor the radical.

$$\begin{gathered} b-1=\sqrt{2\times 2\times 2\times 2\times 3} \\ b-1=\pm 4\sqrt{3} \end{gathered}$$

Solve for b.

$b=1\pm 4\sqrt{3}$

Rewrite to show two solutions.

$$\begin{gathered} b=1+4\sqrt{3}, \\ b=1-4\sqrt{3} \end{gathered}$$