SOLUTION: I am in desperate need of help on this problem. x^1/2-4x^1/4=-3

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Question 279246: I am in desperate need of help on this problem.
x^1/2-4x^1/4=-3
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%281%2F2%29+-+4x%5E%281%2F4%29+=+-3 Solve for x:
If you can make this equation look more like a standard quadratic equation, then you can ease your desperation.
Try a change of variable like this:
x%5E%281%2F4%29+=+y, then x%5E%281%2F2%29+=+y%5E2 Make these substitions to get:
y%5E2-4y+=+-3 Add 3 to both sides to get:
y%5E2-4y%2B3+=+0 Now you can see that you have a standard quadratic equation in y, so now we solve for y.
y%5E2-4y%2B3+=+0 Factor.
%28y-1%29%28y-3%29=+0 so that...
y+=+1 or y+=+3 Now substitute y+=+x%5E%281%2F4%29
x%5E%281%2F4%29+=+1 or x%5E%281%2F4%29+=+3 In both solutions, raise both sides to the 4th power.
%28x%5E%281%2F4%29%29%5E4+=+1%5E4 or %28x%5E%281%2F4%29%29%5E4+=+3%5E4 Evaluate:3%5E4+=+81
highlight%28x+=+1%29 or highlight%28x+=+81%29