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Simplifying 6x4 + 6x2 + -16 = 0 Reorder the terms: -16 + 6x2 + 6x4 = 0 Solving -16 + 6x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + 3x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + 3x2 + 3x4)' equal to zero and attempt to solve: Simplifying -8 + 3x2 + 3x4 = 0 Solving -8 + 3x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + x2 + x4 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + x2 + 2.666666667 + x4 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + x2 + x4 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x2 + x4 = 0 + 2.666666667 x2 + x4 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 x2 + x4 = 2.666666667 The x term is x2. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x4 = 2.666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x4 = 2.666666667 + 0.25 Combine like terms: 2.666666667 + 0.25 = 2.916666667 1.25 + x4 = 2.916666667 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x2 + 0.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x2 + 0.5 = 1.707825128 Simplifying x2 + 0.5 = 1.707825128 Reorder the terms: 0.5 + x2 = 1.707825128 Solving 0.5 + x2 = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = 1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 1.707825128 + -0.5 x2 = 1.707825128 + -0.5 Combine like terms: 1.707825128 + -0.5 = 1.207825128 x2 = 1.207825128 Simplifying x2 = 1.207825128 Take the square root of each side: x = {-1.099010977, 1.099010977}Subproblem 2
x2 + 0.5 = -1.707825128 Simplifying x2 + 0.5 = -1.707825128 Reorder the terms: 0.5 + x2 = -1.707825128 Solving 0.5 + x2 = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x2 = -1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -1.707825128 + -0.5 x2 = -1.707825128 + -0.5 Combine like terms: -1.707825128 + -0.5 = -2.207825128 x2 = -2.207825128 Simplifying x2 = -2.207825128 Reorder the terms: 2.207825128 + x2 = -2.207825128 + 2.207825128 Combine like terms: -2.207825128 + 2.207825128 = 0.000000000 2.207825128 + x2 = 0.000000000 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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