SOLUTION: Solve: 2√(1-x) - 3√(2x-1) = 1

Algebra ->  Average -> SOLUTION: Solve: 2√(1-x) - 3√(2x-1) = 1      Log On


   

Question 975126: Solve: 2√(1-x) - 3√(2x-1) = 1
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
2sqrt%281-x%29=3sqrt%282x-1%29%2B1
4%281-x%29=9%282x-1%29%2B6sqrt%282x-1%29%2B1
4%281-x%29-9%282x-1%29-1=6sqrt%282x-1%29, notice that the indicated distributive property multiplications have not yet been performed; only still isolating the irrational expression.

LeftSide, 4-4x-18x%2B9
-22x%2B13
13-22x

Revised equation,
13-22x=6sqrt%282x-1%29
Square both sides,
169-2%2A13%2A22x%2B22%5E2%2Ax%5E2=36%282x-1%29
169-572x%2B484x%5E2=72x-36
484x%5E2-572x%2B169-72x%2B36=0
highlight_green%28484x%5E2-644x%2B205=0%29

Use the general solution for a quadratic equation.
Discriminant, 644%5E2-4%2A484%2A205=17856=8%2A2232=8%2A8%2A279=8%2A8%2A9%2A31
sqrt%288%2A8%2A9%2A31%29=24sqrt%2831%29
-
x=%28644%2B-+24sqrt%2831%29%29%2F%282%2A484%29

x=%28644%2B-+24sqrt%2831%29%29%2F%282%2A4%2A121%29

highlight%28x=%28161%2B-+6sqrt%2831%29%29%2F%28242%29%29