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Simplifying -16x2 + -2x4 = -32 Solving -16x2 + -2x4 = -32 Solving for variable 'x'. Reorder the terms: 32 + -16x2 + -2x4 = -32 + 32 Combine like terms: -32 + 32 = 0 32 + -16x2 + -2x4 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(16 + -8x2 + -1x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(16 + -8x2 + -1x4)' equal to zero and attempt to solve: Simplifying 16 + -8x2 + -1x4 = 0 Solving 16 + -8x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 8x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 8x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 8x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 8x2 + x4 = 0 + 16 8x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 8x2 + x4 = 16 The x term is 8x2. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x2 + 16 + x4 = 16 + 16 Reorder the terms: 16 + 8x2 + x4 = 16 + 16 Combine like terms: 16 + 16 = 32 16 + 8x2 + x4 = 32 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x2 + 4) equal to 5.656854249 and -5.656854249.Subproblem 1
x2 + 4 = 5.656854249 Simplifying x2 + 4 = 5.656854249 Reorder the terms: 4 + x2 = 5.656854249 Solving 4 + x2 = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 5.656854249 + -4 x2 = 5.656854249 + -4 Combine like terms: 5.656854249 + -4 = 1.656854249 x2 = 1.656854249 Simplifying x2 = 1.656854249 Take the square root of each side: x = {-1.287188506, 1.287188506}Subproblem 2
x2 + 4 = -5.656854249 Simplifying x2 + 4 = -5.656854249 Reorder the terms: 4 + x2 = -5.656854249 Solving 4 + x2 = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = -5.656854249 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -5.656854249 + -4 x2 = -5.656854249 + -4 Combine like terms: -5.656854249 + -4 = -9.656854249 x2 = -9.656854249 Simplifying x2 = -9.656854249 Reorder the terms: 9.656854249 + x2 = -9.656854249 + 9.656854249 Combine like terms: -9.656854249 + 9.656854249 = 0.000000000 9.656854249 + 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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