SOLUTION: Solve for x. Check for extraneous solutions. ( square root of 2x-1 ) -1 = square root of 1-x Everytime I try to solve it, I get different answers.

Algebra ->  Test -> SOLUTION: Solve for x. Check for extraneous solutions. ( square root of 2x-1 ) -1 = square root of 1-x Everytime I try to solve it, I get different answers.       Log On


   

Question 706075: Solve for x. Check for extraneous solutions.
( square root of 2x-1 ) -1 = square root of 1-x
Everytime I try to solve it, I get different answers.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Best guess is you want this?
sqrt%282x-1%29-1=sqrt%281-x%29

square both sides, 2x-1-2sqrt%282x-1%29%2B1=1-x
2sqrt%282x-1%29=3x-1
Square both sides again,
.
8x-4=9x%5E2-6x%2B1
.
highlight%289x%5E2-14x%2B5=0%29

Directly use quadratic formula solution:
x=%2814%2Bsqrt%2814%5E2-4%2A9%2A5%29%29%2F%282%2A9%29 OR x=%2814-sqrt%2814%5E2-4%2A9%2A5%29%29%2F%282%2A9%29
ANSWER: highlight%28x=1%29 OR highlight%28x=5%2F9%29