SOLUTION: x+5(squareroot x)-10=2(squareroot x)

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Question 180271: x+5(squareroot x)-10=2(squareroot x)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x%2B5%2Asqrt%28x%29-10 = 2%2Asqrt%28x%29
these are like terms so subtract 5%2Asqrt%28x%29 from both sides (gets rid of the radical on the left)
x - 10 = 2%2Asqrt%28x%29-5%2Asqrt%28x%29
:
x - 10 = -3%2Asqrt%28x%29
Square both sides
(x-10)^2 = 9x
FOIL
x^2 - 20x + 100 = 9x
;
x^2 - 20x - 9x + 100 = 0
:
x^2 - 29x + 100 = 0
factors to:
(x-4)(x-25) = 0
Two solutions
x = +4
x= +25
:
Important to check each solution in the original equation
for x = 4
4%2B5%2Asqrt%284%29-10 = 2%2Asqrt%284%29
4 + 5(2) - 10 = 2(2)
4 = 4; a good solution
;
for x = 25
25%2B5%2Asqrt%2825%29-10 = 2%2Asqrt%2825%29
25 + 5(5) - 10 = 2(5)
Not a good solution
:
x = 4 is the only solution