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Simplifying 6x4 + 4x2 + -12 = 0 Reorder the terms: -12 + 4x2 + 6x4 = 0 Solving -12 + 4x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 2x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 2x2 + 3x4)' equal to zero and attempt to solve: Simplifying -6 + 2x2 + 3x4 = 0 Solving -6 + 2x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 0.6666666667x2 + x4 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.6666666667x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 0.6666666667x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.6666666667x2 + x4 = 0 + 2 0.6666666667x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 0.6666666667x2 + x4 = 2 The x term is 0.6666666667x2. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x2 + 0.1111111112 + x4 = 2 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x2 + x4 = 2 + 0.1111111112 Combine like terms: 2 + 0.1111111112 = 2.1111111112 0.1111111112 + 0.6666666667x2 + x4 = 2.1111111112 Factor a perfect square on the left side: (x2 + 0.3333333334)(x2 + 0.3333333334) = 2.1111111112 Calculate the square root of the right side: 1.452966315 Break this problem into two subproblems by setting (x2 + 0.3333333334) equal to 1.452966315 and -1.452966315.Subproblem 1
x2 + 0.3333333334 = 1.452966315 Simplifying x2 + 0.3333333334 = 1.452966315 Reorder the terms: 0.3333333334 + x2 = 1.452966315 Solving 0.3333333334 + x2 = 1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = 1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = 1.452966315 + -0.3333333334 x2 = 1.452966315 + -0.3333333334 Combine like terms: 1.452966315 + -0.3333333334 = 1.1196329816 x2 = 1.1196329816 Simplifying x2 = 1.1196329816 Take the square root of each side: x = {-1.05812711, 1.05812711}Subproblem 2
x2 + 0.3333333334 = -1.452966315 Simplifying x2 + 0.3333333334 = -1.452966315 Reorder the terms: 0.3333333334 + x2 = -1.452966315 Solving 0.3333333334 + x2 = -1.452966315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x2 = -1.452966315 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x2 = -1.452966315 + -0.3333333334 x2 = -1.452966315 + -0.3333333334 Combine like terms: -1.452966315 + -0.3333333334 = -1.7862996484 x2 = -1.7862996484 Simplifying x2 = -1.7862996484 Reorder the terms: 1.7862996484 + x2 = -1.7862996484 + 1.7862996484 Combine like terms: -1.7862996484 + 1.7862996484 = 0.0000000000 1.7862996484 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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