SOLUTION: Solve the equation for x: x^4-32x^2-256=0 Thank you!

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Question 856859: Solve the equation for x: x^4-32x^2-256=0
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Make the substitution:
+z+=+x%5E2+
and
+z%5E2+=+x%5E4+
--------------------------
+z%5E2+-+32z+-+256+=+0+
+z+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-32+
+c+=+-256+
+z+=+%28+-%28-32%29+%2B-+sqrt%28+%28-32%29%5E2+-+4%2A1%2A%28-256%29+%29%29+%2F+%282%2A1%29+
+z+=+%28+32+%2B-+sqrt%28+1024+%2B+1024+%29%29+%2F+2+
+z+=+%28+32+%2B-+sqrt%28+2048+%29%29+%2F+2+
+z+=+%28+32+%2B-+32%2Asqrt%282%29%29+%2F+2+
+z+=+16%2A%28+1+%2B+sqrt%282%29+%29+
+z+=+16%2A%28+1+-+sqrt%282%29+%29+
-------------------------------
+z+=+x%5E2+
+x+=+sqrt%28z%29+
+x+=+-sqrt%28z%29+
--------------------------
+x+=+4%2Asqrt%28+1+%2B+sqrt%282%29+%29+
+x+=+-4%2Asqrt%28+1+%2B+sqrt%282%29+%29+
+x+=+4%2Asqrt%28+1+-+sqrt%282%29+%29+ ( imaginary root )
+x+=+-4%2Asqrt%28+1+-+sqrt%282%29+%29+ ( imaginary root )
You can plug these back in to check