Solve the equation. \sqrt{(n^{2}-4n-4)}=n

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

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Expert Answer

Adnaan Franks
Answered 2021-09-30 Author has 6714 answers
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.
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