Completing the Square

[tlcourtney]

Here's my problem:
x[sup:qnar0g8i]2[/sup:qnar0g8i]-6x-11=0

This is what I think the solution is but I am wrong:
x[sup:qnar0g8i]2[/sup:qnar0g8i]-6x+3[sup:qnar0g8i]2[/sup:qnar0g8i]=11
x[sup:qnar0g8i]2[/sup:qnar0g8i]-6x+9=11+9
(x-3)[sup:qnar0g8i]2[/sup:qnar0g8i]=20
x-3=+ or -20 squared

The book says it equals 3+2 5 squared and 3-2 5 squared

 

[Mrspi]

Here's my problem:
x[sup:1v5rznx5]2[/sup:1v5rznx5]-6x-11=0

This is what I think the solution is but I am wrong:
x[sup:1v5rznx5]2[/sup:1v5rznx5]-6x+3[sup:1v5rznx5]2[/sup:1v5rznx5]=11+ 3[sup:1v5rznx5]2[/sup:1v5rznx5]
x[sup:1v5rznx5]2[/sup:1v5rznx5]-6x+9=11+9
(x-3)[sup:1v5rznx5]2[/sup:1v5rznx5]=20
x-3=+ or -20 squared<-----wrong. You have taken the square root of both sides, so you should have
x - 3 = +/- SQUARE ROOT(20)
x = 3 +/- sqrt(20)

Now...simplify square root of 20. sqrt(20) = sqrt(4*5) = sqrt(4)*sqrt(5) or 2 sqrt(5)
x = 3 +/- 2 sqrt(5)


The book says it equals 3+2 5 squared and 3-2 5 squared