SOLUTION: I need the formula for this equation: the square root of 2x-1 minus the square root of x-5=3. Thanks

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Question 212167: I need the formula for this equation: the square root of 2x-1 minus the square root of x-5=3. Thanks
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the square root of 2x-1 minus the square root of x-5=3.
:
sqrt%282x-1%29+-+sqrt%28x-5%29 = 3
;
Add sqrt%28x-5%29 to both sides
sqrt%282x-1%29 = 3+%2B+sqrt%28x-5%29
:
Square both sides: FOIL the right side
2x - 1 = 9+%2B+6%2Asqrt%28x-5%29+%2B+%28x-5%29
:
2x - 1 = x+%2B+9+-+5+%2B+6%2Asqrt%28x-5%29
:
2x - 1 = x+%2B+4+%2B+6%2Asqrt%28x-5%29
:
2x - x - 1 - 4 = +6%2Asqrt%28x-5%29
:
x - 5 = +6%2Asqrt%28x-5%29
:
Square both sides; FOIL the left side:
x^2 - 10x + 25 = 36(x-5)
:
x^2 - 10x + 25 = 36x - 180
:
x^2 - 10x - 36x + 25 + 180 = 0
:
x^2 - 46x + 205 = 0; our old friend the quadratic equation
Factor
(x-41)(x-5) = 0
Two solutions
x = 41
x = 5
:
:
Check solutions in original equation:
x = 41
sqrt%282%2841%29-1%29+-+sqrt%2841-5%29 = 3
sqrt%2882-1%29+-+sqrt%2836%29 = 3
sqrt%2881%29+-+sqrt%2836%29 = 3
9 - 6 = 3; a good solution
and
x = 5
sqrt%282%285%29-1%29+-+sqrt%285+-+5%29 = 3
sqrt%289%29+-+sqrt%280%29 = 3
3 - 0 = 3; also a good solution