#### Answer

$x=\pm2\sqrt{10}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
5x^2-200=0
,$ use the properties of equality and express the equation in the form $x^2=c.$ Then take the square root of both sides (Square Root Property) and simplify the resulting radical.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
5x^2=200
\\\\
x^2=\dfrac{200}{5}
\\\\
x^2=40
.\end{array}
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{40}
.\end{array}
Writing the radicand as an expression that contains a factor that is a perfect power of the index and then extracting the root of that factor result to
\begin{array}{l}\require{cancel}
x=\pm\sqrt{4\cdot10}
\\\\
x=\pm\sqrt{(2)^2\cdot10}
\\\\
x=\pm2\sqrt{10}
.\end{array}