SOLUTION: PLEASE HELP!!! Solve -x^4+200=102x^2. I have to show my work and I don't understand how to do this. It is from a worksheet. Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: PLEASE HELP!!! Solve -x^4+200=102x^2. I have to show my work and I don't understand how to do this. It is from a worksheet. Thanks      Log On


   

Question 166175: PLEASE HELP!!!
Solve -x^4+200=102x^2.
I have to show my work and I don't understand how to do this. It is from a worksheet.
Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
-x%5E4%2B200=102x%5E2
-x%5E4-102x%5E2%2B200=0
x%5E4%2B102x%5E2-200=0
Looks kind of like a quadratic equation.
Use a substitution.
u=x%5E2
x%5E4%2B102x%5E2-200=0
u%5E2%2B102u-200=0
Now solve using the quadratic formula,
u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
u+=+%28-102+%2B-+sqrt%28+102%5E2-4%2A1%2A%28-200%29+%29%29%2F%282%2A1%29+
u+=+%28-102+%2B-+sqrt%28+10404%2B800+%29%29%2F%282%29+
u+=+%28-102+%2B-+sqrt%2811204%29%29%2F%282%29+
u+=+%28-102+%2B-+105.85%29%2F%282%29+
Let's look at both solutions separately,
u%5B1%5D+=+%28-102+%2B+105.85%29%2F%282%29+
u%5B1%5D+=+%283.85%29%2F%282%29+
u%5B1%5D+=+1.925+
%28x%29%5E2+=+1.925+
x=+0+%2B-+1.387
x%5B1%5D=+1.387
x%5B2%5D=+-1.387
.
.
.
u%5B2%5D+=+%28-102+-+105.85%29%2F%282%29+
u%5B2%5D+=+%28-207.85%29%2F%282%29+
u%5B2%5D+=+-103.925
%28x%29%5E2+=+-103.925
x=+0+%2B-+10.19i
x%5B3%5D=+10.19i
x%5B4%5D=+-10.19i