-8x^4+24x^2-6=0

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Solution for -8x^4+24x^2-6=0 equation:


Simplifying
-8x4 + 24x2 + -6 = 0

Reorder the terms:
-6 + 24x2 + -8x4 = 0

Solving
-6 + 24x2 + -8x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 12x2 + -4x4) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-3 + 12x2 + -4x4)' equal to zero and attempt to solve: Simplifying -3 + 12x2 + -4x4 = 0 Solving -3 + 12x2 + -4x4 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -3x2 + x4 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -3x2 + -0.75 + x4 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -3x2 + x4 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -3x2 + x4 = 0 + -0.75 -3x2 + x4 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -3x2 + x4 = -0.75 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -0.75 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -0.75 + 2.25 Combine like terms: -0.75 + 2.25 = 1.5 2.25 + -3x2 + x4 = 1.5 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x2 + -1.5 = 1.224744871 Simplifying x2 + -1.5 = 1.224744871 Reorder the terms: -1.5 + x2 = 1.224744871 Solving -1.5 + x2 = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.224744871 + 1.5 x2 = 1.224744871 + 1.5 Combine like terms: 1.224744871 + 1.5 = 2.724744871 x2 = 2.724744871 Simplifying x2 = 2.724744871 Take the square root of each side: x = {-1.650680124, 1.650680124}

Subproblem 2

x2 + -1.5 = -1.224744871 Simplifying x2 + -1.5 = -1.224744871 Reorder the terms: -1.5 + x2 = -1.224744871 Solving -1.5 + x2 = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.224744871 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.224744871 + 1.5 x2 = -1.224744871 + 1.5 Combine like terms: -1.224744871 + 1.5 = 0.275255129 x2 = 0.275255129 Simplifying x2 = 0.275255129 Take the square root of each side: x = {-0.524647624, 0.524647624}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.650680124, 1.650680124, -0.524647624, 0.524647624}

Solution

x = {-1.650680124, 1.650680124, -0.524647624, 0.524647624}

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