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Simplifying 6x4 + 8x2 + -12 = 0 Reorder the terms: -12 + 8x2 + 6x4 = 0 Solving -12 + 8x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 4x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 4x2 + 3x4)' equal to zero and attempt to solve: Simplifying -6 + 4x2 + 3x4 = 0 Solving -6 + 4x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 1.333333333x2 + x4 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.333333333x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 1.333333333x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.333333333x2 + x4 = 0 + 2 1.333333333x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 1.333333333x2 + x4 = 2 The x term is 1.333333333x2. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x2 + 0.4444444442 + x4 = 2 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x2 + x4 = 2 + 0.4444444442 Combine like terms: 2 + 0.4444444442 = 2.4444444442 0.4444444442 + 1.333333333x2 + x4 = 2.4444444442 Factor a perfect square on the left side: (x2 + 0.6666666665)(x2 + 0.6666666665) = 2.4444444442 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x2 + 0.6666666665) equal to 1.56347192 and -1.56347192.Subproblem 1
x2 + 0.6666666665 = 1.56347192 Simplifying x2 + 0.6666666665 = 1.56347192 Reorder the terms: 0.6666666665 + x2 = 1.56347192 Solving 0.6666666665 + x2 = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x2 = 1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x2 = 1.56347192 + -0.6666666665 x2 = 1.56347192 + -0.6666666665 Combine like terms: 1.56347192 + -0.6666666665 = 0.8968052535 x2 = 0.8968052535 Simplifying x2 = 0.8968052535 Take the square root of each side: x = {-0.946998022, 0.946998022}Subproblem 2
x2 + 0.6666666665 = -1.56347192 Simplifying x2 + 0.6666666665 = -1.56347192 Reorder the terms: 0.6666666665 + x2 = -1.56347192 Solving 0.6666666665 + x2 = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x2 = -1.56347192 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x2 = -1.56347192 + -0.6666666665 x2 = -1.56347192 + -0.6666666665 Combine like terms: -1.56347192 + -0.6666666665 = -2.2301385865 x2 = -2.2301385865 Simplifying x2 = -2.2301385865 Reorder the terms: 2.2301385865 + x2 = -2.2301385865 + 2.2301385865 Combine like terms: -2.2301385865 + 2.2301385865 = 0.0000000000 2.2301385865 + 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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