Question 181939
I'm going to use the quadratic formula:



{{{x^2+8x=0}}} Start with the given equation.



{{{x^2+8x+0=0}}} Add 0 to the left side (this does NOT change the equation)



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, and {{{c=0}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(8) +- sqrt( (8)^2-4(1)(0) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=0}}}



{{{x = (-8 +- sqrt( 64-4(1)(0) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-0 ))/(2(1))}}} Multiply {{{4(1)(0)}}} to get {{{0}}}



{{{x = (-8 +- sqrt( 64 ))/(2(1))}}} Subtract {{{0}}} from {{{64}}} to get {{{64}}}



{{{x = (-8 +- sqrt( 64 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 8)/(2)}}} Take the square root of {{{64}}} to get {{{8}}}. 



{{{x = (-8 + 8)/(2)}}} or {{{x = (-8 - 8)/(2)}}} Break up the expression. 



{{{x = (0)/(2)}}} or {{{x =  (-16)/(2)}}} Combine like terms. 



{{{x = 0}}} or {{{x = -8}}} Simplify. 



So the answers are {{{x = 0}}} or {{{x = -8}}}