Question 635127


{{{x^2-24x+144=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-24x+144}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-24}}}, and {{{C=144}}}



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



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



{{{x = (-(-24) +- sqrt( (-24)^2-4(1)(144) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-24}}}, and {{{C=144}}}



{{{x = (24 +- sqrt( (-24)^2-4(1)(144) ))/(2(1))}}} Negate {{{-24}}} to get {{{24}}}. 



{{{x = (24 +- sqrt( 576-4(1)(144) ))/(2(1))}}} Square {{{-24}}} to get {{{576}}}. 



{{{x = (24 +- sqrt( 576-576 ))/(2(1))}}} Multiply {{{4(1)(144)}}} to get {{{576}}}



{{{x = (24 +- sqrt( 0 ))/(2(1))}}} Subtract {{{576}}} from {{{576}}} to get {{{0}}}



{{{x = (24 +- sqrt( 0 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (24 +- 0)/(2)}}} Take the square root of {{{0}}} to get {{{0}}}. 



{{{x = (24 + 0)/(2)}}} or {{{x = (24 - 0)/(2)}}} Break up the expression. 



{{{x = (24)/(2)}}} or {{{x =  (24)/(2)}}} Combine like terms. 



{{{x = 12}}} or {{{x = 12}}} Simplify. 



So the only solution is {{{x = 12}}}