Question 172883
{{{x^2=5x + 2}}}  Start with the given equation.



{{{x^2-5x = 2}}}  Subtract 5x from both sides.



Take half of the x coefficient 5 to get {{{5/2}}}. Square that value to get {{{25/4}}}


{{{x^2-5x +25/4= 2+25/4}}}  Add {{{25/4}}} to both sides.



{{{x^2-5x +25/4= 33/4}}}  Combine like terms.



{{{(x-5/2)^2 =33/4}}}  Factor {{{x^2-5x +25/4}}} to get {{{(x-5/2)^2}}}



{{{x-5/2=0+-sqrt(33/4)}}} Take the square root of both sides.



{{{x-5/2=sqrt(33/4)}}} or {{{x-5/2=-sqrt(33/4)}}} Break up the "plus/minus" to form two equations.



{{{x-5/2=sqrt(33)/2}}} or {{{x-5/2=-sqrt(33)/2}}}  Simplify the square root.



{{{x=5/2+sqrt(33)/2}}} or {{{x=5/2-sqrt(33)/2}}} Add {{{5/2}}} to both sides.



{{{x=(5+sqrt(33))/(2)}}} or {{{x=(5-sqrt(33))/(2)}}} Combine the fractions.



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Answer:



So the solutions are {{{x=(5+sqrt(33))/(2)}}} or {{{x=(5-sqrt(33))/(2)}}}.