Question 315576


{{{x^2+8x+15=0}}} Start with the given equation.



Notice that the quadratic {{{x^2+8x+15}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=8}}}, and {{{C=15}}}



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)(15) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=8}}}, and {{{C=15}}}



{{{x = (-8 +- sqrt( 64-4(1)(15) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-60 ))/(2(1))}}} Multiply {{{4(1)(15)}}} to get {{{60}}}



{{{x = (-8 +- sqrt( 4 ))/(2(1))}}} Subtract {{{60}}} from {{{64}}} to get {{{4}}}



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



{{{x = (-8 +- 2)/(2)}}} Take the square root of {{{4}}} to get {{{2}}}. 



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



{{{x = (-6)/(2)}}} or {{{x =  (-10)/(2)}}} Combine like terms. 



{{{x = -3}}} or {{{x = -5}}} Simplify. 



So the solutions are {{{x = -3}}} or {{{x = -5}}}