Answer
$x=2\pm\dfrac{2}{3}i$
Work Step by Step
$9x^{2}-36x=-40$
Take out common factor $9$ from the left side of the equation:
$9(x^{2}-4x)=-40$
Take the $9$ to divide the right side of the equation:
$x^{2}-4x=-\dfrac{40}{9}$
Add $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation. In this case, $b=-4$
$x^{2}-4x+\Big(\dfrac{-4}{2}\Big)^{2}=-\dfrac{40}{9}+\Big(\dfrac{-4}{2}\Big)^{2}$
$x^{2}-4x+4=-\dfrac{40}{9}+4$
$x^{2}-4x+4=-\dfrac{4}{9}$
Factor the expression on the left side of the equation, which is a perfect square trinomial:
$(x-2)^{2}=-\dfrac{4}{9}$
Take the square root of both sides of the equation:
$\sqrt{(x-2)^{2}}=\sqrt{-\dfrac{4}{9}}$
$x-2=\pm\dfrac{2}{3}i$
Solve for $x$:
$x=2\pm\dfrac{2}{3}i$
