SOLUTION: Find all real solutions: x^4-16x^2-80=0

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Question 914191: Find all real solutions: x^4-16x^2-80=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +z+=+x%5E2+
+z%5E2+-+16z+-+80+=+0+
complete the square:
+z%5E2+-+16z+%2B+%2816%2F2%29%5E2+=+80+%2B+%2816%2F2%29%5E2+
+z%5E2+-+16z+%2B+64+=+80+%2B+64+
+%28+z+-+8+%29%5E2+=+12%5E2+
+z+-+8+=+12+
+z+=+20+
and also:
+z+-+8+=+-12+
+z+=+-4+
---------------
+z+=+x%5E2+
+20+=+x%5E2+
+x+=+2%2Asqrt%285%29+
+x+=+-2%2Asqrt%285%29+
and
+z+=+x%5E2+
+-4+=+x%5E2+
+x+=+2i+
+x+=+-2i+
these are the 4 solutions
You can plug them back in to check
The real solutions are the first 2