Question 104710
{{{x-2*sqrt(x-3)=3}}} Start with the given equation



{{{-2*sqrt(x-3)=3-x}}} Subtract x from both sides



{{{sqrt(x-3)=(3-x)/-2}}} Divide both sides by -2




{{{x-3=((3-x)/-2)^2}}} Square both sides



Now this is where you went wrong, when you square {{{3-x}}} you need to foil it to get {{{9-6x+x^2}}} instead of {{{9+x^2}}}



{{{x-3=(9-6x+x^2)/4}}} Foil the numerator and square the denominator



{{{x=(9-6x+x^2)/4+3}}} Add 3 to both sides



{{{x=(9-6x+x^2)/4+3(4/4)}}} Multiply 3 by {{{4/4}}} 



{{{x=(9-6x+x^2)/4+12/4}}} Multiply 



{{{x=(9-6x+x^2+12)/4}}} Add the fractions



{{{x=(-6x+x^2+21)/4}}} Combine like terms



{{{4x=-6x+x^2+21}}} Multiply both sides by 4



{{{0=-6x+x^2+21-4x}}} Subtract 4x from both sides



{{{0=x^2+21-10x}}} Combine like terms


{{{0=x^2-10x+21}}} Rearrange the terms



*[invoke quadratic_formula 1, -10, 21, "x"]



So this means the solution set is {7,3}