Question 151501
Start with the given equations.


{{{g(x)=2x^2 -8}}} and {{{k(x) =-x^2 -2}}}



Since {{{g(x)=k(x)}}}, this means that {{{2x^2 -8=-x^2 -2}}}





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



{{{2x^2-8+1x^2+2=0}}} Add {{{x^2}}} to both sides. Add 2 to both sides.



{{{3x^2-6=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=3}}}, {{{b=0}}}, and {{{c=-6}}}



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)(-6) ))/(2(3))}}} Plug in  {{{a=3}}}, {{{b=0}}}, and {{{c=-6}}}



{{{x = (-0 +- sqrt( 0-4(3)(-6) ))/(2(3))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (-0 +- sqrt( 0--72 ))/(2(3))}}} Multiply {{{4(3)(-6)}}} to get {{{-72}}}



{{{x = (-0 +- sqrt( 0+72 ))/(2(3))}}} Rewrite {{{sqrt(0--72)}}} as {{{sqrt(0+72)}}}



{{{x = (-0 +- sqrt( 72 ))/(2(3))}}} Add {{{0}}} to {{{72}}} to get {{{72}}}



{{{x = (-0 +- sqrt( 72 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{x = (-0 +- 6*sqrt(2))/(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(2))/(6)}}} Break up the fraction.  



{{{x = 0 +- sqrt(2)}}} Reduce.  



{{{x = sqrt(2)}}} or {{{x = -sqrt(2)}}} Break up the expression.  



So the answers are {{{x = sqrt(2)}}} or {{{x = -sqrt(2)}}} 



which approximate to {{{x=1.414}}} or {{{x=-1.414}}}