Question 289785
The original quadratic equation: {{{ -x^2-x=7 }}}
First you have to get the quadratic equation to equal to 0.
So you have to subtract 7 on both sides. You should get {{{ -x^2-x-7=0 }}}
It doesn't seem like the quadratic equation can be easily factored.
We have to use the quadratic formula which is {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

In our case,
a= -1
b= -1
c= -7
Plug in the values for the variables.
{{{x = (-(-1) +- sqrt( (-1)^2-4*-1*-7 ))/(2*-1) }}}
Simplify the equation:
{{{x = (1 +- sqrt( 1-28 ))/(-2) }}}
{{{x = (1 +- sqrt( -27 ))/(-2) }}}
The discriminant is less than zero, we can now tell that the solutions are imaginary and should include the symbol i.
{{{x = (1 +- 3 i sqrt3 )/(-2) }}}
{{{x = -1/2 +- (3/2)i sqrt3  }}}