# How do you solve sqrt(x+12)=x?

May 19, 2015

$\sqrt{x + 12} = x$

squaring both the sides
${\left(\sqrt{x + 12}\right)}^{2} = {x}^{2}$
$x + 12 = {x}^{2}$
${x}^{2} - x - 12 = 0$

we can find the roots by Splitting the Middle Term of this expression to factorise it:

${x}^{2} - x - 12 = {x}^{2} - 4 x + 3 x - 12$
$= x \left(x - 4\right) + 3 \left(x - 4\right)$
$= \left(x + 3\right) \left(x - 4\right)$

the solution is $\textcolor{b l u e}{x} = - 3 , \textcolor{b l u e}{x} = 4$