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Simplifying 4x4 + -8x2 + -2 = 0 Reorder the terms: -2 + -8x2 + 4x4 = 0 Solving -2 + -8x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -4x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4x2 + 2x4)' equal to zero and attempt to solve: Simplifying -1 + -4x2 + 2x4 = 0 Solving -1 + -4x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -2x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2x2 + x4 = 0 + 0.5 -2x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2x2 + x4 = 0.5 The x term is -2x2. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x2 + 1 + x4 = 0.5 + 1 Reorder the terms: 1 + -2x2 + x4 = 0.5 + 1 Combine like terms: 0.5 + 1 = 1.5 1 + -2x2 + x4 = 1.5 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x2 + -1) equal to 1.224744871 and -1.224744871.Subproblem 1
x2 + -1 = 1.224744871 Simplifying x2 + -1 = 1.224744871 Reorder the terms: -1 + x2 = 1.224744871 Solving -1 + x2 = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = 1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 1.224744871 + 1 x2 = 1.224744871 + 1 Combine like terms: 1.224744871 + 1 = 2.224744871 x2 = 2.224744871 Simplifying x2 = 2.224744871 Take the square root of each side: x = {-1.491557867, 1.491557867}Subproblem 2
x2 + -1 = -1.224744871 Simplifying x2 + -1 = -1.224744871 Reorder the terms: -1 + x2 = -1.224744871 Solving -1 + x2 = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x2 = -1.224744871 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -1.224744871 + 1 x2 = -1.224744871 + 1 Combine like terms: -1.224744871 + 1 = -0.224744871 x2 = -0.224744871 Simplifying x2 = -0.224744871 Reorder the terms: 0.224744871 + x2 = -0.224744871 + 0.224744871 Combine like terms: -0.224744871 + 0.224744871 = 0.000000000 0.224744871 + 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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