SOLUTION: Solve for x in terms of the other letters. 4x(to the fourth power)y(to the fourth power) + 2x(squared)y(squared) + .75= 0

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Question 213324This question is from textbook college algebra
: Solve for x in terms of the other letters. 4x(to the fourth power)y(to the fourth power) + 2x(squared)y(squared) + .75= 0 This question is from textbook college algebra

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4x(to the fourth power)y(to the fourth power) + 2x(squared)y(squared) + .75= 0
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4x%5E4y%5E4+%2B+2x%5E2y%5E2+%2B+0.75+=+0
Sub x for x^2y^2 to use the onsite solver
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B2x%2B0.75+=+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=%282%29%5E2-4%2A4%2A0.75=-8.

The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -8 is + or - sqrt%28+8%29+=+2.82842712474619.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B2%2Ax%2B0.75+%29

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x%5E2y%5E2+=+%28-1%2Bi%2Asqrt%282%29%29%2F4
x%5E2+=+%28-1%2Bi%2Asqrt%282%29%29%2F4y%5E2
x+=+%2Bsqrt%28%28-1%2Bsqrt%282%29%29%29%2F2y
x+=+-sqrt%28%28-1%2Bsqrt%282%29%29%29%2F2y
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x%5E2y%5E2+=+-%28-1%2Bi%2Asqrt%282%29%29%2F4
x%5E2+=+-%28-1%2Bi%2Asqrt%282%29%29%2F4y%5E2
x+=+%2Bi%2Asqrt%28-1%2Bsqrt%282%29%29%2F2y
x+=+-i%2Asqrt%28-1%2Bsqrt%282%29%29%2F2y