#### Answer

$\color{blue}{\left\{-10, 10\right\}}$

#### Work Step by Step

Subtract $150$ to both sides of the equation to obtain:
$x^2+50-150=150-150
\\x^2-100=0$
Since $100=10^2$, the given equation can be written as:
$x^2-10^2=0$
RECALL:
$a^2-b^2=(a-b)(a+b)$
Factor the binomial using the formula above to obtain:
$(x-10)(x+10)=0$
Use the Zero-Factor Property by equating each factor to zero to obtain:
$x-10=0$ or $x+10=0$
Solve each equation to obtain:
$x-10=0
\\x=0+10
\\x=10$
or
$x+10=0
\\x=0-10
\\x=-10$
Therefore, the solution set is $\color{blue}{\left\{-10, 10\right\}}$.