Question 78248
{{{-4x^2 + 8x=7}}}
{{{-4x^2 + 8x-7=0}}} Subtract 7 from both sides

*[invoke completing_the_square -4, 8, -7]

So now we have

{{{-4(x-1)^2-3=0}}}
{{{-4(x-1)^2=3}}} Add 3 to both sides
{{{(x-1)^2=3/-4}}} Divide both sides by -4
{{{x-1=0+-sqrt(-3/4)}}} Take the square root of both sides
{{{x=0+-sqrt(-3/4)+1}}} Add 1 to both sides

Since we cannot take the square root of a negative number, we must factor out a negative 1

{{{x=0+-sqrt(-1)sqrt(3/4)+1}}} 

Now we'll let {{{i=sqrt(-1)}}} and say

{{{x=0+-sqrt(3/4)i+1}}}

{{{x=0+-sqrt(3)/2*i+1}}} Reduce the denominator

So our answer is 

{{{x=sqrt(3)/2*i+1}}} or {{{x=-sqrt(3)/2*i+1}}}