Question 145102


{{{-x^2+ 2x = 8}}} Start with the given equation.



{{{-x^2+ 2x -8=0}}} Get all terms to the left side.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=-1}}}, {{{b=2}}}, and {{{c=-8}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(2) +- sqrt( (2)^2-4(-1)(-8) ))/(2(-1))}}} Plug in  {{{a=-1}}}, {{{b=2}}}, and {{{c=-8}}}



{{{x = (-2 +- sqrt( 4-4(-1)(-8) ))/(2(-1))}}} Square {{{2}}} to get {{{4}}}. 



{{{x = (-2 +- sqrt( 4-32 ))/(2(-1))}}} Multiply {{{4(-1)(-8)}}} to get {{{32}}}



{{{x = (-2 +- sqrt( -28 ))/(2(-1))}}} Subtract {{{32}}} from {{{4}}} to get {{{-28}}}



{{{x = (-2 +- sqrt( -28 ))/(-2)}}} Multiply {{{2}}} and {{{-1}}} to get {{{-2}}}. 



{{{x = (-2 +- 2i*sqrt(7))/(-2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (-2)/(-2) +- (2i*sqrt(7))/(-2)}}} Break up the fraction.  



{{{x = 1 +- -1sqrt(7)*i}}} Reduce.  



{{{x = 1-1sqrt(7)*i}}} or {{{x = 1+1sqrt(7)*i}}} Break up the expression.  



So our answers are {{{x = 1-1sqrt(7)*i}}} or {{{x = 1+1sqrt(7)*i}}} 



which approximate to {{{x=-1.646*i}}} or {{{x=3.646*i}}}