SOLUTION: What is 4 more than the square root of 2x equals x? Please include all work.

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Question 482954: What is 4 more than the square root of 2x equals x? Please include all work.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
What is 4 more than the square root of 2x equals x?
sqrt%282x%29 + 4 = x
:
subtract 4 from both sides
sqrt%282x%29 = x - 4
:
square both sides
2x = (x-4)^2
:
FOIL (x-4(x-4)
2x = x^2 - 8x + 16
:
Subtract 2x from both sides
0 = x^2 - 8x - 2x + 16
:
A quadratic equation
x^2 - 10x + 16 = 0
:
Factor to
(x-8)(x-2) = 0
:
Two solutions
x = 8
x = 2
:
Check both solutions in original equation
x=8
sqrt%282%288%29%29 + 4 = 8
sqrt%2816%29 + 4 = 8; a good solution
and
x=2
sqrt%282%282%29%29 + 4 = 2
sqrt%284%29 + 4 = 2
2 + 4 does not = 2, therefore not a good solutions