# How do you solve for m in sqrtm – 10n = n-5?

Oct 11, 2016

$m = 121 {n}^{2} + 110 n + 25$

#### Explanation:

As $\sqrt{m} - 10 n = n - 5$, adding $10 n$ to both sides

$\sqrt{m} - 10 n + 10 n = 10 n + n - 5$

or $\sqrt{m} = 11 n - 5$

and $m = {\left(11 n + 5\right)}^{2}$

= ${\left(11 n\right)}^{2} + 2 \times 11 n \times 5 + {5}^{2}$

= $121 {n}^{2} + 110 n + 25$