Answer
$x=25$
Work Step by Step
Using the properties of equality, the given equation, $
4\sqrt{x}+5=x
,$ is equivalent to
\begin{array}{l}\require{cancel}
4\sqrt{x}=x-5
.\end{array}
Squaring both sides of the equation and then using the properties of equality, we obtain:
\begin{array}{l}\require{cancel}\left(
4\sqrt{x}
\right)^2=\left(
x-5
\right)^2
\\\\
16x=(x)^2+2(x)(-5)+(-5)^2
\\\\
16x=x^2-10x+25
\\\\
0=x^2+(-10x-16x)+25
\\\\
0=x^2-26x+25
\\\\
(x-25)(x-1)=0
\\\\
x=\{1,25\}
.\end{array}
Upon checking, only $
x=25
$ satisfies the original equation.
