Answer
$m=-5-\sqrt{2}, -5+\sqrt{2}$
Work Step by Step
The left side of the given equation, $
m^2+10m+25=2
,$ is a perfect square trinomial. Using $a^2+2ab+b^2=(a+b)^2,$ the given equation is equivalent to
\begin{align*}
(m)^2+2(5)(m)+(5)^2&=2
\\
(m+5)^2&=2
.\end{align*}
Taking the square root of both sides (Square Root Principle) and solving for the variable, the equation above is equivalent to
\begin{align*}
m+5&=\pm\sqrt{2}
\\
m&=-5\pm\sqrt{2}
.\end{align*}
Hence, the solutions to the equation $
m^2+10m+25=2
$ are $
m=-5-\sqrt{2}, -5+\sqrt{2}
.$
