48x^4-2x^2-1=0

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Solution for 48x^4-2x^2-1=0 equation:


Simplifying
48x4 + -2x2 + -1 = 0

Reorder the terms:
-1 + -2x2 + 48x4 = 0

Solving
-1 + -2x2 + 48x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -8x2)(1 + -6x2) = 0

Subproblem 1

Set the factor '(-1 + -8x2)' equal to zero and attempt to solve: Simplifying -1 + -8x2 = 0 Solving -1 + -8x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -8x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -8x2 = 0 + 1 -8x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -8x2 = 1 Divide each side by '-8'. x2 = -0.125 Simplifying x2 = -0.125 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(1 + -6x2)' equal to zero and attempt to solve: Simplifying 1 + -6x2 = 0 Solving 1 + -6x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x2 = 0 + -1 -6x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -6x2 = -1 Divide each side by '-6'. x2 = 0.1666666667 Simplifying x2 = 0.1666666667 Take the square root of each side: x = {-0.408248291, 0.408248291}

Solution

x = {-0.408248291, 0.408248291}

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