Answer
$x\approx-7.47
\text{ and }
x\approx1.47$
Work Step by Step
Using the properties of equality, the given equation, $
x^2=11-6x
,$ is equivalent to
\begin{align*}
x^2+6x-11=0
\end{align*}
In the equation above, $a=
1
,$ $b=
6
,$ and $c=
-11
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-6\pm\sqrt{6^2-4(1)(-11)}}{2(1)}
\\\\&=
\dfrac{-6\pm\sqrt{36+44}}{2}
\\\\&=
\dfrac{-6\pm\sqrt{80}}{2}
\\\\&=
\dfrac{-6\pm\sqrt{16\cdot5}}{2}
\\\\&=
\dfrac{-6\pm4\sqrt{5}}{2}
\\\\&=
\dfrac{-\cancel6^3\pm\cancel4^2\sqrt{5}}{\cancel2^1}
&\text{ (divide by $2$)}
\\\\&=
\dfrac{-3\pm2\sqrt{5}}{1}
\\\\&=
-3\pm2\sqrt{5}
\end{align*}
\begin{array}{lcl}
&\Rightarrow
-3-2\sqrt{5} &\text{ OR }& -3+2\sqrt{5}
\\\\&
\approx-7.47 && \approx1.47
\end{array}
Hence, the solutions are $
x\approx-7.47
\text{ and }
x\approx1.47
.$
