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Simplifying 16x4 + -128x2 + -256 = 0 Reorder the terms: -256 + -128x2 + 16x4 = 0 Solving -256 + -128x2 + 16x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(-16 + -8x2 + x4) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-16 + -8x2 + x4)' equal to zero and attempt to solve: Simplifying -16 + -8x2 + x4 = 0 Solving -16 + -8x2 + x4 = 0 Begin completing the square. 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 = 9.656854249 x2 = 9.656854249 Simplifying x2 = 9.656854249 Take the square root of each side: x = {-3.107547948, 3.107547948}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 = -1.656854249 x2 = -1.656854249 Simplifying x2 = -1.656854249 Reorder the terms: 1.656854249 + x2 = -1.656854249 + 1.656854249 Combine like terms: -1.656854249 + 1.656854249 = 0.000000000 1.656854249 + 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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