SOLUTION: 8x^(4)-6x^(2)-5=0

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Question 204232: 8x^(4)-6x^(2)-5=0
Found 2 solutions by Earlsdon, stanbon:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
SOlve for x:
You can expect to get four solutions to this "quartic" equation. First, rewrite the equation so as to appear like a "quadratic" equation in x%5E2:
8%28x%5E2%29%5E2-6%28x%5E2%29-5+=+0 Factor this "quadratic"equation.
%284x%5E2-5%29%282x%5E2%2B1%29+=+0 Apply the zero product rule:
4x%5E2-5+=+0 or 2x%5E2%2B1+=+0 so that...
4x%5E2+=+5 or 2x%5E2+=+-1 and...
highlight%28x%5E2+=+5%2F4%29 or highlight_green%28x%5E2+=+-1%2F2%29 Now take the square root of both sides of these two intermdediate solutions.
highlight%28x+=+sqrt%285%29%2F2%29 or highlight%28x+=+-sqrt%285%29%2F2%29 or
highlight_green%28x+=+sqrt%28-1%2F2%29%29 or highlight_green%28x+=+-sqrt%28-1%2F2%29%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
8x^(4)-6x^(2)-5=0
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Factor the left side:
8x^4 - 10x^2 + 4x^2 - 5 = 0
Factor the 1st 2 and the last two terms separately to get:
2x^2(4x^2-5)+ (4x^2-5) = 0
(4x^2-5)(2x^2+1) = 0
Solve for "x":
4x^2 = 5 or 2x^2+1 = 0
x^2 = 5/4 or x^2 = -1/2
x = +/-sqrt(5/4) or x = +-isqrt(1/2)
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Cheers,
Stan H.