Question

Solve using the square root property.

$n^2+10n+25=12$

Short answer

The solution is$n=\pm 2\sqrt{3}-5$.

Step-by-step solution

Step 1. Given information.

The given equation is$n^2+10n+25=12$.

Step 2. Apply the square root property.

The property states that if$x=k^2$, then$x=\pm \sqrt{k}$.

Step 3. Simplify the equation.

$$\begin{gathered} n^2+10n+25=12 \\ {n}^2+2·n·5+5^2=12 \\ {\left(n+5\right)}^2=12 \\ n+5=\pm \sqrt{12} \\ n+5=\pm 2\sqrt{3} \\ n=\pm 2\sqrt{3}-5 \end{gathered}$$

Step 4. Simplified answer.

Hence, the required solution is$n=\pm 2\sqrt{3}-5$.