Question 77972
#22
{{{-9(x-3)^2 = -7}}}

{{{(x-3)^2 = 7/9}}} Divide both sides by -9

{{{x-3 =0+- sqrt(7/9)}}} Take the square root of both sides

{{{x-3 =0+- sqrt(7)/3}}} Reduce the denominator

{{{x =0+- sqrt(7)/3+3}}} Add 3 to both sides so our solution is



#33

*[invoke completing_the_square 2, -4, -11]

So we now have

{{{0=2(x-1)^2-13}}}

{{{13=2(x-1)^2}}} Add 13 to both sides

{{{13/2=(x-1)^2}}} Divide both sides by 2

{{{0+-sqrt(13/2)=x-1}}} Take the square root of both sides

{{{0+-sqrt(13/2)+1=x}}} Add 1 to both sides

So our answer is

{{{x=0+-sqrt(13/2)+1}}}