Answer
The solution is $x=9$
Work Step by Step
$\sqrt{4x}-x+3=0$
Leave the square root alone on the left side of the equation:
$\sqrt{4x}=x-3$
Square both sides:
$(\sqrt{4x})^{2}=(x-3)^{2}$
$4x=x^{2}-6x+9$
Take $4x$ to the right side and simplify:
$0=x^{2}-6x+9-4x$
$0=x^{2}-10x+9$
Rearrange:
$x^{2}-10x+9=0$
Solve by factoring:
$(x-1)(x-9)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x-1=0$
$x=1$
$x-9=0$
$x=9$
Check the solutions found by substituting them into the original equation:
$x=1$
$\sqrt{4(1)}-1+3=0$
$2-1+3=0$
$4\ne0$ False
$x=9$
$\sqrt{4(9)}-9+3=0$
$6-9+3=0$
$0=0$ True
The solution is $x=9$
