How do you solve sqrt(3m+28) =m?

Jul 20, 2015

color(blue)( m=7

Explanation:

$\sqrt{3 m + 28} = m$

Squaring both sides
${\left(\sqrt{3 m + 28}\right)}^{2} = {m}^{2}$

$3 m + 28 = {m}^{2}$

${m}^{2} - 3 m - 28 = 0$

Factorising by splitting the middle term (in order to find the solutions)**

${m}^{2} - \textcolor{g r e e n}{3 m} - 28 = 0$

${m}^{2} - \textcolor{g r e e n}{7 m + 4 m} - 28 = 0$

$m \left(m - 7\right) + 4 \left(m - 7\right) = 0$

$\left(m + 4\right) \left(m - 7\right) = 0$

Upon equating the factors with zero we can obtain solutions:

$m + 4 = 0 , m = - 4$
This solution is not applicable as square root of an expression cannot be negative

So the solution is
$\left(m - 7\right) = 0 , m = 7$