## help with equation involving x^(3/2)

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
mricks152
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Joined: Tue Jan 24, 2012 11:26 pm
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### help with equation involving x^(3/2)

I need to solve the following equation:

2x^2 + 15x^(3/2) + 155x + 75 = 0

Any ideas?

nona.m.nona
Posts: 285
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: help with equation involving x^(3/2)

mricks152 wrote:I need to solve the following equation:

2x^2 + 15x^(3/2) + 155x + 75 = 0

Any ideas?

One might try restating the current variable and powers in terms of y = sqrt[x]:

$2\left(\sqrt{x}\right)^4\, +\, 15\left(\sqrt{x}\right)^3\, +\, 155\left(\sqrt{x}\right)^2\, +\, 75\, =\, 0$

$2y^4\, +\, 15y^3\, +\, 155y^2\, +\, 75\, =\, 0$

Then apply standard techniques for solving polynomial equations.