#### Answer

$x=\left\{ -4,1 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\sqrt{x^2+3x}-2=0
,$ isolate the radical expression. Then square both sides and express in the form $ax^2+bx+c=0.$ Use concepts of solving quadratic equations to find the values of $x$. Finally, do checking of the solutions with the original equation.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{x^2+3x}=2
.\end{array}
Squaring both sides of the given equation results to
\begin{array}{l}\require{cancel}
x^2+3x=2^2
\\\\
x^2+3x=4
.\end{array}
In the form $ax^2+bx+c=0,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x^2+3x-4=0
.\end{array}
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the factored form of the equation above is
\begin{array}{l}\require{cancel}
(x+4)(x-1)=0
.\end{array}
Equating each factor to zero (Zero Product Property) results to
\begin{array}{l}\require{cancel}
x+4=0
\\\\\text{OR}\\\\
x-1=0
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
x+4=0
\\\\
x=-4
\\\\\text{OR}\\\\
x-1=0
\\\\
x=1
.\end{array}
Upon checking, $
x=\left\{ -4,1 \right\}
$ satisfy the original equation.