Question 207432


{{{x^2+11x+24=0}}} Start with the given equation.



Notice that the quadratic {{{x^2+11x+24}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=11}}}, and {{{C=24}}}



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



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



{{{x = (-(11) +- sqrt( (11)^2-4(1)(24) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=11}}}, and {{{C=24}}}



{{{x = (-11 +- sqrt( 121-4(1)(24) ))/(2(1))}}} Square {{{11}}} to get {{{121}}}. 



{{{x = (-11 +- sqrt( 121-96 ))/(2(1))}}} Multiply {{{4(1)(24)}}} to get {{{96}}}



{{{x = (-11 +- sqrt( 25 ))/(2(1))}}} Subtract {{{96}}} from {{{121}}} to get {{{25}}}



{{{x = (-11 +- sqrt( 25 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-11 +- 5)/(2)}}} Take the square root of {{{25}}} to get {{{5}}}. 



{{{x = (-11 + 5)/(2)}}} or {{{x = (-11 - 5)/(2)}}} Break up the expression. 



{{{x = (-6)/(2)}}} or {{{x =  (-16)/(2)}}} Combine like terms. 



{{{x = -3}}} or {{{x = -8}}} Simplify. 



So the solutions are {{{x = -3}}} or {{{x = -8}}}