Answer
$x=3$
Work Step by Step
Using the properties of equality, the given equation, $
x^2=6x-9
,$ is equivalent to
\begin{align*}
x^2-6x+9&=0
.\end{align*}
Using $ax^2+bx+c=0,$ the equation above has $a=
1
,$ $b=
-6
,$ and $c=
9
.$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}
x&=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(1)(9)}}{2(1)}
\\\\&=
\dfrac{6\pm\sqrt{36-36}}{2}
\\\\&=
\dfrac{6\pm0}{2}
\\\\&=
\dfrac{6}{2}
\\\\&=
3
.\end{align*}
The solution is $
x=3
.$