Answer
The solutions are $x=1\pm\dfrac{\sqrt{3}}{2}i$
Work Step by Step
$-4x^{2}+8x=7$
Divide the whole equation by $-4$:
$-\dfrac{1}{4}(-4x^{2}+8x=7)$
$x^{2}-2x=-\dfrac{7}{4}$
Complete the square by adding $\Big(\dfrac{b}{2}\Big)^{2}$ to both sides of the equation and simplifying. In this case, $b=-2$
$x^{2}-2x+\Big(-\dfrac{2}{2}\Big)^{2}=-\dfrac{7}{4}+\Big(-\dfrac{2}{2}\Big)^{2}$
$x^{2}-2x+1=-\dfrac{7}{4}+1$
$x^{2}-2x+1=-\dfrac{3}{4}$
Factor the left side of the equation, which is a perfect square trinomial:
$(x-1)^{2}=-\dfrac{3}{4}$
Take the square root of both sides:
$\sqrt{(x-1)^{2}}=\pm\sqrt{-\dfrac{3}{4}}$
$x-1=\pm\dfrac{\sqrt{3}}{2}i$
Solve for $x$:
$x=1\pm\dfrac{\sqrt{3}}{2}i$
