Question

Solve the quadratic equation using square root property.

$n^2+8n+16=27$

Short answer

The solutions are$n=-4\pm 3\sqrt{3}$.

Step-by-step solution

Given Information.    

The Given equation is $n^2+8n+16=27$.

Factor the trinomial.   

$$\begin{gathered} n^2+2\left(4\right)n+(4{)}^2=27 \\ (n+4{)}^2=27 \end{gathered}$$

Use square root property.

$$\begin{gathered} n+4=\pm \sqrt{27} \\ n+4=\pm 3\sqrt{3} \end{gathered}$$

Isolate the term.

$n=-4\pm 3\sqrt{3}$

Thus, the solutions are$n=-4\pm 3\sqrt{3}$.