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Simplifying 64x4 + -4x2 + -16 = 0 Reorder the terms: -16 + -4x2 + 64x4 = 0 Solving -16 + -4x2 + 64x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -1x2 + 16x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -1x2 + 16x4)' equal to zero and attempt to solve: Simplifying -4 + -1x2 + 16x4 = 0 Solving -4 + -1x2 + 16x4 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -0.0625x2 + x4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.0625x2 + 0.25 + x4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.0625x2 + x4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.0625x2 + x4 = 0 + 0.25 -0.0625x2 + x4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.0625x2 + x4 = 0.25 The x term is -0.0625x2. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x2 + 0.0009765625 + x4 = 0.25 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x2 + x4 = 0.25 + 0.0009765625 Combine like terms: 0.25 + 0.0009765625 = 0.2509765625 0.0009765625 + -0.0625x2 + x4 = 0.2509765625 Factor a perfect square on the left side: (x2 + -0.03125)(x2 + -0.03125) = 0.2509765625 Calculate the square root of the right side: 0.500975611 Break this problem into two subproblems by setting (x2 + -0.03125) equal to 0.500975611 and -0.500975611.Subproblem 1
x2 + -0.03125 = 0.500975611 Simplifying x2 + -0.03125 = 0.500975611 Reorder the terms: -0.03125 + x2 = 0.500975611 Solving -0.03125 + x2 = 0.500975611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x2 = 0.500975611 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x2 = 0.500975611 + 0.03125 x2 = 0.500975611 + 0.03125 Combine like terms: 0.500975611 + 0.03125 = 0.532225611 x2 = 0.532225611 Simplifying x2 = 0.532225611 Take the square root of each side: x = {-0.729537943, 0.729537943}Subproblem 2
x2 + -0.03125 = -0.500975611 Simplifying x2 + -0.03125 = -0.500975611 Reorder the terms: -0.03125 + x2 = -0.500975611 Solving -0.03125 + x2 = -0.500975611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x2 = -0.500975611 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x2 = -0.500975611 + 0.03125 x2 = -0.500975611 + 0.03125 Combine like terms: -0.500975611 + 0.03125 = -0.469725611 x2 = -0.469725611 Simplifying x2 = -0.469725611 Reorder the terms: 0.469725611 + x2 = -0.469725611 + 0.469725611 Combine like terms: -0.469725611 + 0.469725611 = 0.000000000 0.469725611 + 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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