Answer
$x=-5$ and $x=2$
Work Step by Step
The given equation is
$x^2+7x=-10$
Add $10$ to each side.
$x^2+7x+10=-10+10$
Simplify.
$x^2+7x+10=0$
Graph the related function.
$f(x)=x^2+7x+10$
The $x-$intercepts are $-5$ and $-2$.
Check $x=-5$.
$\Rightarrow x^2+7x+10=0$
$\Rightarrow (-5)^2+7(-5)+10=0$
$\Rightarrow 25-35+10=0$
$\Rightarrow 35-35=0$
$\Rightarrow 0=0$
True.
Check $x=-2$.
$\Rightarrow x^2+7x+10=0$
$\Rightarrow (-2)^2+7(-2)+10=0$
$\Rightarrow 4-14+10=0$
$\Rightarrow 14-14=0$
$\Rightarrow 0=0$
True.
Hence, the solutions are $x=-5$ and $x=2$.
