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Simplifying x4 + -1x2 + -32 = 0 Reorder the terms: -32 + -1x2 + x4 = 0 Solving -32 + -1x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -1x2 + 32 + x4 = 0 + 32 Reorder the terms: -32 + 32 + -1x2 + x4 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -1x2 + x4 = 0 + 32 -1x2 + x4 = 0 + 32 Combine like terms: 0 + 32 = 32 -1x2 + x4 = 32 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 = 32 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 32 + 0.25 Combine like terms: 32 + 0.25 = 32.25 0.25 + -1x2 + x4 = 32.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x2 + -0.5) equal to 5.678908346 and -5.678908346.Subproblem 1
x2 + -0.5 = 5.678908346 Simplifying x2 + -0.5 = 5.678908346 Reorder the terms: -0.5 + x2 = 5.678908346 Solving -0.5 + x2 = 5.678908346 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 = 5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 5.678908346 + 0.5 x2 = 5.678908346 + 0.5 Combine like terms: 5.678908346 + 0.5 = 6.178908346 x2 = 6.178908346 Simplifying x2 = 6.178908346 Take the square root of each side: x = {-2.485741005, 2.485741005}Subproblem 2
x2 + -0.5 = -5.678908346 Simplifying x2 + -0.5 = -5.678908346 Reorder the terms: -0.5 + x2 = -5.678908346 Solving -0.5 + x2 = -5.678908346 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 = -5.678908346 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -5.678908346 + 0.5 x2 = -5.678908346 + 0.5 Combine like terms: -5.678908346 + 0.5 = -5.178908346 x2 = -5.178908346 Simplifying x2 = -5.178908346 Reorder the terms: 5.178908346 + x2 = -5.178908346 + 5.178908346 Combine like terms: -5.178908346 + 5.178908346 = 0.000000000 5.178908346 + 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.
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