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

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Answer 1 · 2017-06-06T13:20:01

See a solution process below:

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

$(sqrt(m - 10n))^2 = (n - 5)^2$

$m - 10n = (n - 5)^2$

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

$(a - b)^2 = a^2 - 2ab + b^2$

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

$m - 10n = n^2 - 2n5 + 5^2$

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

Now, add $color(red)(10n)$ to each side of the equation to solve for $m$ :

$m - 10n + color(red)(10n) = n^2 - 10n + color(red)(10n) + 25$

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

$m = n^2 + 25$

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