Question 149055

{{{x^2-x=736}}} Start with the given equation.



{{{x^2-x-736=0}}} Get all terms to the left side.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-1}}}, and {{{c=-736}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-1) +- sqrt( (-1)^2-4(1)(-736) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-1}}}, and {{{c=-736}}}



{{{x = (1 +- sqrt( (-1)^2-4(1)(-736) ))/(2(1))}}} Negate {{{-1}}} to get {{{1}}}. 



{{{x = (1 +- sqrt( 1-4(1)(-736) ))/(2(1))}}} Square {{{-1}}} to get {{{1}}}. 



{{{x = (1 +- sqrt( 1--2944 ))/(2(1))}}} Multiply {{{4(1)(-736)}}} to get {{{-2944}}}



{{{x = (1 +- sqrt( 1+2944 ))/(2(1))}}} Rewrite {{{sqrt(1--2944)}}} as {{{sqrt(1+2944)}}}



{{{x = (1 +- sqrt( 2945 ))/(2(1))}}} Add {{{1}}} to {{{2944}}} to get {{{2945}}}



{{{x = (1 +- sqrt( 2945 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (1+sqrt(2945))/(2)}}} or {{{x = (1-sqrt(2945))/(2)}}} Break up the expression.  



So our answers are {{{x = (1+sqrt(2945))/(2)}}} or {{{x = (1-sqrt(2945))/(2)}}} 



which approximate to {{{x=27.634}}} or {{{x=-26.634}}} 



I'm not sure what you're looking for, but if you aren't expecting to get an irrational answer, then try {{{y=378}}}