Answer
$x=\left\{ \dfrac{6-2i}{3},\dfrac{6+2i}{3} \right\}$
Work Step by Step
Using the completing the square method, the solutions of the given quadratic equation, $
9x^2-36x=-40
,$ is
\begin{array}{l}\require{cancel}
\dfrac{1}{9}\cdot (9x^2-36x)=(-40)\cdot\dfrac{1}{9}
\\\\
x^2-4x=-\dfrac{40}{9}
\\\\
x^2-4x+\left( \dfrac{-4}{2} \right)^2=-\dfrac{40}{9}+\left( \dfrac{-4}{2} \right)^2
\\\\
x^2-4x+4=-\dfrac{40}{9}+4
\\\\
(x-2)^2=-\dfrac{40}{9}+\dfrac{36}{9}
\\\\
(x-2)^2=-\dfrac{4}{9}
\\\\
x-2=\pm\sqrt{-\dfrac{4}{9}}
\\\\
x-2=\pm \dfrac{2}{3}i
\\\\
x=2\pm \dfrac{2}{3}i
\\\\
x=\dfrac{6}{3}\pm \dfrac{2}{3}i
\\\\
x=\dfrac{6\pm2i}{3}
.\end{array}
Hence, $
x=\left\{ \dfrac{6-2i}{3},\dfrac{6+2i}{3} \right\}
.$
