SOLUTION: x^4-5x^-36=0 How do I solve this.

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Question 322829: x^4-5x^-36=0 How do I solve this.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What's the exponent on the 2nd term?
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If it's 2:
It's a quadratic in x^2
x^4-5x^2-36=0
You can factor it.
(x^2 + 4)*(x^2 - 9) = 0
x^2 = 9
x = ± 3
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x^2 = -4
x = ± 2i
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You can use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-36+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A1%2A-36=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-5%29-sqrt%28+169+%29%29%2F2%5C1+=+-4

Quadratic expression 1x%5E2%2B-5x%2B-36 can be factored:
1x%5E2%2B-5x%2B-36+=+%28x-9%29%2A%28x--4%29
Again, the answer is: 9, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-36+%29

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The x given is actually x^2, so see above.