Please help me cant figure this out!!?

Question

I need major help with this I am really confused!

Solve the equation by extraction of roots.
3/4(x -6)^2 =18

3 is over 4, and ^ = 2nd power

Answer 1

3/4(x -6)^2 =18
3/4(x^2-12x+36) = 18 (x4/3)
x^2-12x+36 = 24
x^2-12x+12 = 0
(x-6)(x-6) = 0
x1=6, x2=6

Answer 2

1. Multiply both sides by recip of 3/4 (4/3 is recip) to get rid of fraction on the left side, which gives us:

(x-6)^2 = 18 * (4/3)


2. Simplify

(x-6)^2 = 24


3. Ok, now you need to get rid of the ^2 on the left. So what is the opposide of sqared? Square root. So, take the square root of both sides. You'll end up with:

x - 6 = sqrt(24)


4. This is where you start doing the extraction of roots. So what's a root of 24 that can easily be pulled out of the square root? Start with finding small numbers you know have square roots. In this case, it's 4, here's the next step:

x - 6 = sqrt( 4 * 6)

5. Then we separate the 2 roots

x - 6 = sqrt(4) * sqrt (6)


6. We can easily take the square root of 4. It's 2.


x - 6 = 2 * sqrt(6)


7. 6 doesn't have an easy square root, so we've gone as far with the problem as we can. Move the 6 over and you get your answer.

x = 2*sqrt(6) + 6

Answer 3

30