SOLUTION: How do I solve for x or even turn x^1/2-9x^1/4+20=0 into a quadratic equation? none of my books would give me a similar example.

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Question 1141405: How do I solve for x or even turn x^1/2-9x^1/4+20=0 into a quadratic equation? none of my books would give me a similar example.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%281%2F2%29-9x%5E%281%2F4%29%2B20=0

If p=x%5E%281%2F4%29, then p%5E2=x%5E%281%2F4%2B1%2F4%29=x%5E%281%2F2%29;


substituting that
p%5E2-9p%2B20=0
and maybe this is factorable or maybe not. Try and see. Otherwise, use general solution formula method. Continue from there.









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Let cross%28p=x%5E%281%2F2%29%29


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by the other tutor is incorrect.

x^(1/2) is the square of x^(1/4); so this is a quadratic equation in which the "variable" is x^(1/4). With experience most students can solve it in its given form. But for most students it helps to define a new variable y=x^(1/4). Then the equation is

y%5E2-9y%2B20+=+0

That equation is easily solved by factoring.

(Then remember the values of y are not the answers to the original question....)