Question 184090
{{{x^2 - 12x =45}}} Start with the given equation



What the book is doing is completing the square on the left side (which will help isolate "x").



{{{x^2 - 12x +36=45+36}}} Take half of the "x" coefficient -12 to get -6. Square -6 to get 36. Add this value to both sides.



{{{x^2 - 12x +36=81}}} Combine like terms.



{{{(x-6)^2=81}}} Factor the left side



{{{x-6=0+- sqrt(81)}}} Take the square root of both sides.



{{{x-6=sqrt(81)}}} or {{{x-6=-sqrt(81)}}} Break up the "plus/minus"



{{{x-6=9}}} or {{{x-6=-9}}} Take the square root of 81 to get 9



{{{x=6+9}}} or {{{x=6-9}}} Add 6 to both sides.



{{{x=15}}} or {{{x=-3}}} Combine like terms.



So the solutions are {{{x=15}}} or {{{x=-3}}}