Question

Solve the quadratic equation using square root property.

$(n-7{)}^2-8=64$

Short answer

The solutions are$n=7\pm 6\sqrt{2}$.

Step-by-step solution

Given Information.   

The Given equation is$(n-7{)}^2-8=64$.

Isolate the binomial term. 

$$\begin{gathered} (n-7{)}^2=64+8 \\ (n-7{)}^2=72 \end{gathered}$$

Use the Square Root Property. 

$n-7=\pm \sqrt{72}$

Factor the radical.

$$\begin{gathered} n-7=\pm \sqrt{2\times 2\times 2\times 3\times 3} \\ n-7=\pm 6\sqrt{2} \end{gathered}$$

Solve for n.

$n=7\pm 6\sqrt{2}$

Rewrite to show two solutions.

$$\begin{gathered} n=7+6\sqrt{2}, \\ n=7-6\sqrt{2} \end{gathered}$$