SOLUTION: What is 4+ the square root of 2x-5=x

Question 56124: What is 4+ the square root of 2x-5=x
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
What is 4+ the square root of 2x-5=x
:
4 + SqRt(2x-5) = x
:
SqRt(2x-5) = x - 4; subtracted 4 from both sides
:
2x - 5 = x^2 - 8x + 16; squared both sides, FOILed (x-4)^2
:
0 = x^2 - 8x - 2x + 16 + 5, arrange on the right,
:
x^2 - 10x + 21 = 0; our old friend, the quadratic equation
:
Easily factored:
(x-3)(x-7) = 0
x = +3
x = +7
:
Check both solutions, especially when dealing with square roots.
4 + SqRt(2(3) - 5) = 3
4 + SqRt(1) = 5 not 3 as required, x=3 is not a solution
:
Try x = 7
4 + SqRt(2(7) - 5) = 7
4 + SqRt(9) = 7; x = 7 is a good solution

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