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Simplifying 4x4 + -2x2 + -4 = 0 Reorder the terms: -4 + -2x2 + 4x4 = 0 Solving -4 + -2x2 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -1x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x2 + 2x4)' equal to zero and attempt to solve: Simplifying -2 + -1x2 + 2x4 = 0 Solving -2 + -1x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -0.5x2 + x4 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5x2 + 1 + x4 = 0 + 1 Reorder the terms: -1 + 1 + -0.5x2 + x4 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5x2 + x4 = 0 + 1 -0.5x2 + x4 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5x2 + x4 = 1 The x term is -0.5x2. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x2 + 0.0625 + x4 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5x2 + x4 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5x2 + x4 = 1.0625 Factor a perfect square on the left side: (x2 + -0.25)(x2 + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x2 + -0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
x2 + -0.25 = 1.030776406 Simplifying x2 + -0.25 = 1.030776406 Reorder the terms: -0.25 + x2 = 1.030776406 Solving -0.25 + x2 = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = 1.030776406 + 0.25 x2 = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 x2 = 1.280776406 Simplifying x2 = 1.280776406 Take the square root of each side: x = {-1.131713924, 1.131713924}Subproblem 2
x2 + -0.25 = -1.030776406 Simplifying x2 + -0.25 = -1.030776406 Reorder the terms: -0.25 + x2 = -1.030776406 Solving -0.25 + x2 = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x2 = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x2 = -1.030776406 + 0.25 x2 = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 x2 = -0.780776406 Simplifying x2 = -0.780776406 Reorder the terms: 0.780776406 + x2 = -0.780776406 + 0.780776406 Combine like terms: -0.780776406 + 0.780776406 = 0.000000000 0.780776406 + 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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