# How do you solve for a in sqrt(m – 10n) = n-5?

Jun 6, 2017

See a solution process below:

#### Explanation:

First, square each side of the equation to eliminate the radical:

${\left(\sqrt{m - 10 n}\right)}^{2} = {\left(n - 5\right)}^{2}$

$m - 10 n = {\left(n - 5\right)}^{2}$

We can then square the right side of the equation using this rule:

${\left(a - b\right)}^{2} = {a}^{2} - 2 a b + {b}^{2}$

Substituting $n$ for $a$ and $5$ for $b$ gives:

$m - 10 n = {n}^{2} - 2 n 5 + {5}^{2}$

$m - 10 n = {n}^{2} - 10 n + 25$

Now, add $\textcolor{red}{10 n}$ to each side of the equation to solve for $m$:

$m - 10 n + \textcolor{red}{10 n} = {n}^{2} - 10 n + \textcolor{red}{10 n} + 25$

$m - 0 = {n}^{2} - 0 + 25$

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