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Simplifying 16x4 + -16x2 + -4 = 0 Reorder the terms: -4 + -16x2 + 16x4 = 0 Solving -4 + -16x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -4x2 + 4x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -4x2 + 4x4)' equal to zero and attempt to solve: Simplifying -1 + -4x2 + 4x4 = 0 Solving -1 + -4x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1x2 + x4 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1x2 + 0.25 + x4 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1x2 + x4 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1x2 + x4 = 0 + 0.25 -1x2 + x4 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1x2 + x4 = 0.25 The x term is -1x2. 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. -1x2 + 0.25 + x4 = 0.25 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 0.25 + -1x2 + x4 = 0.5 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
x2 + -0.5 = 0.707106781 Simplifying x2 + -0.5 = 0.707106781 Reorder the terms: -0.5 + x2 = 0.707106781 Solving -0.5 + x2 = 0.707106781 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 = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.707106781 + 0.5 x2 = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 x2 = 1.207106781 Simplifying x2 = 1.207106781 Take the square root of each side: x = {-1.098684113, 1.098684113}Subproblem 2
x2 + -0.5 = -0.707106781 Simplifying x2 + -0.5 = -0.707106781 Reorder the terms: -0.5 + x2 = -0.707106781 Solving -0.5 + x2 = -0.707106781 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 = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.707106781 + 0.5 x2 = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 x2 = -0.207106781 Simplifying x2 = -0.207106781 Reorder the terms: 0.207106781 + x2 = -0.207106781 + 0.207106781 Combine like terms: -0.207106781 + 0.207106781 = 0.000000000 0.207106781 + 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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