 # Solve the equation. \sqrt{(n^{2}-4n-4)}=n bobbie71G 2021-09-29 Answered
Solve the equation.
$$\displaystyle\sqrt{{{\left({n}^{{{2}}}-{4}{n}-{4}\right)}}}={n}$$

• Questions are typically answered in as fast as 30 minutes

### Plainmath recommends

• Get a detailed answer even on the hardest topics.
• Ask an expert for a step-by-step guidance to learn to do it yourself. Adnaan Franks
Step 1
To solve the equation $$\displaystyle\sqrt{{{\left({n}^{{{2}}}-{4}{n}-{4}\right)}}}={n}$$, take square on both sides of the equation to remove square root.
$$\displaystyle\sqrt{{{\left({n}^{{{2}}}-{4}{n}-{4}\right)}}}={n}$$
$$\displaystyle{\left[\sqrt{{{\left({n}^{{{2}}}-{4}{n}-{4}\right)}}}\right]}^{{{2}}}={n}^{{{2}}}$$
$$\displaystyle{\left({n}^{{{2}}}-{4}{n}-{4}\right)}={n}^{{{2}}}$$
$$\displaystyle{n}^{{{2}}}-{4}{n}-{4}={n}^{{{2}}}$$...(1)
Step 2
Subtract $$\displaystyle{n}^{{{2}}}$$ on both sides of the equation and simplify to get zero on the right hand side of equation (1).
$$\displaystyle{n}^{{{2}}}-{4}{n}-{4}={n}^{{{2}}}$$
$$\displaystyle{n}^{{{2}}}-{4}{n}-{4}-{n}^{{{2}}}={n}^{{{2}}}-{n}^{{{2}}}$$
$$\displaystyle{n}^{{{2}}}-{n}^{{{2}}}-{4}{n}-{4}={0}$$
0-4n-4=0
-4n-4=0...(2)
Step 3
Add 4 on both sides of equation (2) to isolate variable term.
-4n-4=0
-4n-4+4=0+4
-4n=4...(3)
Step 4
Divide by -4 on both sides of equation (3) to isolate variable n and get the value of n.
-4n=4
$$\displaystyle{\frac{{-{4}{n}}}{{-{4}}}}={\frac{{{4}}}{{-{4}}}}$$
n=-1
Therefore the solution of the equation is n=−1.