Question 337494
{{{2(x-4)^2+x^2=x(x+50)-46x}}} Start with the given equation.



{{{2(x^2-8x+16)+x^2=x(x+50)-46x}}} FOIL.



{{{2x^2-16x+32+x^2=x^2+50x-46x}}} Distribute.



{{{2x^2-16x+32+x^2-1x^2-50x+46x=0}}} Get every term to the left side.



{{{2x^2-20x+32=0}}} Combine like terms.



Notice that the quadratic {{{2x^2-20x+32}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=2}}}, {{{B=-20}}}, and {{{C=32}}}



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



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



{{{x = (-(-20) +- sqrt( (-20)^2-4(2)(32) ))/(2(2))}}} Plug in  {{{A=2}}}, {{{B=-20}}}, and {{{C=32}}}



{{{x = (20 +- sqrt( (-20)^2-4(2)(32) ))/(2(2))}}} Negate {{{-20}}} to get {{{20}}}. 



{{{x = (20 +- sqrt( 400-4(2)(32) ))/(2(2))}}} Square {{{-20}}} to get {{{400}}}. 



{{{x = (20 +- sqrt( 400-256 ))/(2(2))}}} Multiply {{{4(2)(32)}}} to get {{{256}}}



{{{x = (20 +- sqrt( 144 ))/(2(2))}}} Subtract {{{256}}} from {{{400}}} to get {{{144}}}



{{{x = (20 +- sqrt( 144 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (20 +- 12)/(4)}}} Take the square root of {{{144}}} to get {{{12}}}. 



{{{x = (20 + 12)/(4)}}} or {{{x = (20 - 12)/(4)}}} Break up the expression. 



{{{x = (32)/(4)}}} or {{{x =  (8)/(4)}}} Combine like terms. 



{{{x = 8}}} or {{{x = 2}}} Simplify. 



So the solutions are {{{x = 8}}} or {{{x = 2}}} 



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