SOLUTION: Please help solve the following equation using Quadratic Form (NOT formula): {{{2x^4-10x^2=-8}}}

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Please help solve the following equation using Quadratic Form (NOT formula): {{{2x^4-10x^2=-8}}}      Log On


   



Question 327388: Please help solve the following equation using Quadratic Form (NOT formula):
2x%5E4-10x%5E2=-8

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2x^4-10x^2=-8
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2x^4 - 10x^2 + 8 = 0
x^4 - 5x^2 + 4 = 0
Factor:
(x^2-4)(x^2-1) = 0
(x-2)(x+2)(x-1)(x+1)= 0
x = 2 or -2 or 1 or -1
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Cheers,
Stan H.
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Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Temporarily substitute y+=+x%5E2 so now you have:
2y%5E2-10y+=+-8 Add 8 to both sides.
2y%5E2-10y+%2B8+=+0 So now you have a quadratic equation in y. Factor a 2.
2%28y%5E2-5y%2B4%29+=+0 so...
y%5E2-5y%2B4+=+0 This will factor nicely into...
%28y-1%29%28y-4%29+=+0 and from the zero product rule you get...
y-1+=+0 or y-4+=+0 therefore...
y+=+1 or y+=+4 Re-substtute y+=+x%5E2
x%5E2+=+1 or x%5E2+=+4 Taking the square root of both of these, we get...
x+=+1 or x+=+-1 or x+=+2 or x+=+-2