SOLUTION: If sq root(3-x) = 1 - sq root(2x), then 9x^2 = (A) 5 (B) 8 (C) 2 - 3x (D) 12 - 4x (E) 20x - 4 thanks for your help

Algebra ->  Square-cubic-other-roots -> SOLUTION: If sq root(3-x) = 1 - sq root(2x), then 9x^2 = (A) 5 (B) 8 (C) 2 - 3x (D) 12 - 4x (E) 20x - 4 thanks for your help      Log On


   

Question 174652: If sq root(3-x) = 1 - sq root(2x), then 9x^2 =
(A) 5
(B) 8
(C) 2 - 3x
(D) 12 - 4x
(E) 20x - 4
thanks for your help
Answer by SAT Math Tutor(36) About Me  (Show Source):
You can put this solution on YOUR website!
First, square both sides of the equation to get:
1. 3 - x = 1 - 2sqrt%282x%29 + 2x
2. 3 - x = 1 - sqrt%288x%29 + 2x
Then, move 2x to the left hand side and 3 to the right hand side:
3. -3x = -2 - sqrt%288x%29
Next, we will square both sides again, but first note that:
4. 3x - 2 = sqrt%288x%29
We will use that in a second, now square both sides from step 3:
5. 9x^2 = 4 + 4sqrt%288x%29 + 8x
Now, plug in what we have for step 4 into step 5:
6. 9x^2 = 4 + 4(3x - 2) + 8x
Simplify:
9x^2 = 4 + 12x - 8 + 8x
9x^2 = 20x - 4