SOLUTION: Solve the equation by making an appropriate substitution. 2x^1/2

SOLUTION: Solve the equation by making an appropriate substitution. 2x^1/2 - 5x^1/4 -25 = 0

Question 248598: Solve the equation by making an appropriate substitution. 2x^1/2 - 5x^1/4 -25 = 0

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve the equation by making an appropriate substitution. 2x^1/2 - 5x^1/4 -25 = 0
Let r = x^(1/4)
Substitute r for x^(1/4) and you have
2r^2 - 5r - 25 = 0
Factor this to
(2r+5)(r-5) = 0
Two solutions
2r = -5
r = -2.5
and
r = 5
:
go back to x
x^(1/4) = -2.5
Raise both side to the 4th power
x = (-2.5)^4
x = +39.0625
(This solution does not work; try it on a calc)
and
r = 5
x^(1/4) = 5
x = 5^4
x = 625; a good solution
:
Check this solution on a calc, enter
2(625^(1/2)) - 5(625^(1/4)) - 25 = 0
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