Question 548465


{{{-x^2+4=2x^2-5}}} Start with the given equation.



{{{-x^2+4-2x^2+5=0}}} Get every term to the left side.



{{{-3x^2+9=0}}} Combine like terms.



Notice that the quadratic {{{-3x^2+9}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=-3}}}, {{{B=0}}}, and {{{C=9}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(0) +- sqrt( (0)^2-4(-3)(9) ))/(2(-3))}}} Plug in  {{{A=-3}}}, {{{B=0}}}, and {{{C=9}}}



{{{x = (-0 +- sqrt( 0-4(-3)(9) ))/(2(-3))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (-0 +- sqrt( 0--108 ))/(2(-3))}}} Multiply {{{4(-3)(9)}}} to get {{{-108}}}



{{{x = (-0 +- sqrt( 0+108 ))/(2(-3))}}} Rewrite {{{sqrt(0--108)}}} as {{{sqrt(0+108)}}}



{{{x = (-0 +- sqrt( 108 ))/(2(-3))}}} Add {{{0}}} to {{{108}}} to get {{{108}}}



{{{x = (-0 +- sqrt( 108 ))/(-6)}}} Multiply {{{2}}} and {{{-3}}} to get {{{-6}}}. 



{{{x = (-0 +- 6*sqrt(3))/(-6)}}} 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 = (-0)/(-6) +- (6*sqrt(3))/(-6)}}} Break up the fraction.  



{{{x = 0 +- -1*sqrt(3)}}} Reduce.  



{{{x = 0-1*sqrt(3)}}} or {{{x = 0+1*sqrt(3)}}} Break up the expression.  



So the solutions are {{{x = -sqrt(3)}}} or {{{x = sqrt(3)}}}