Question 185628


{{{x^2+20=4x}}} Start with the given equation.



{{{x^2+20-4x=0}}} Subtract 4x from both sides.



{{{x^2-4x+20=0}}} Rearrange the terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-4}}}, and {{{c=20}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-4) +- sqrt( (-4)^2-4(1)(20) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-4}}}, and {{{c=20}}}



{{{x = (4 +- sqrt( (-4)^2-4(1)(20) ))/(2(1))}}} Negate {{{-4}}} to get {{{4}}}. 



{{{x = (4 +- sqrt( 16-4(1)(20) ))/(2(1))}}} Square {{{-4}}} to get {{{16}}}. 



{{{x = (4 +- sqrt( 16-80 ))/(2(1))}}} Multiply {{{4(1)(20)}}} to get {{{80}}}



{{{x = (4 +- sqrt( -64 ))/(2(1))}}} Subtract {{{80}}} from {{{16}}} to get {{{-64}}}



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



{{{x = (4 +- 8*i)/(2)}}} Take the square root of {{{-64}}} to get {{{8*i}}}. 



{{{x = (4 + 8*i)/(2)}}} or {{{x = (4 - 8*i)/(2)}}} Break up the expression. 



{{{x = (4)/(2) + (8*i)/(2)}}} or {{{x =  (4)/(2) - (8*i)/(2)}}} Break up the fraction for each case. 



{{{x = 2+4*i}}} or {{{x =  2-4*i}}} Reduce. 



{{{x = 2+4*i}}} or {{{x = 2-4*i}}} Simplify. 



So the answers are {{{x = 2+4*i}}} or {{{x = 2-4*i}}}