Answer
$x=1
\text{ and }
x=10$
Work Step by Step
Using the properties of equality, the given equation, $
x^2=11x-10
,$ is equivalent to
\begin{align*}
x^2-11x+10&=0
\end{align*}
In the equation above, $a=
1
,$ $b=
-11
,$ and $c=
10
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-11)\pm\sqrt{(-11)^2-4(1)(10)}}{2(1)}
\\\\&=
\dfrac{11\pm\sqrt{121-40}}{2}
\\\\&=
\dfrac{11\pm\sqrt{81}}{2}
\\\\&=
\dfrac{11\pm9}{2}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
\dfrac{11-9}{2} &\text{ OR }& \dfrac{11+9}{2}
\\\\&
=\dfrac{2}{2} && =\dfrac{20}{2}
\\\\&
=1 && =10
\end{array}
Hence, the solutions are $
x=1
\text{ and }
x=10
.$
