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Simplifying x4 + x2 + -88 = 0 Reorder the terms: -88 + x2 + x4 = 0 Solving -88 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + x2 + 88 + x4 = 0 + 88 Reorder the terms: -88 + 88 + x2 + x4 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + x2 + x4 = 0 + 88 x2 + x4 = 0 + 88 Combine like terms: 0 + 88 = 88 x2 + x4 = 88 The x term is x2. 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. x2 + 0.25 + x4 = 88 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 88 + 0.25 Combine like terms: 88 + 0.25 = 88.25 0.25 + x2 + x4 = 88.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 88.25 Calculate the square root of the right side: 9.394147114 Break this problem into two subproblems by setting (x2 + 0.5) equal to 9.394147114 and -9.394147114.Subproblem 1
x2 + 0.5 = 9.394147114 Simplifying x2 + 0.5 = 9.394147114 Reorder the terms: 0.5 + x2 = 9.394147114 Solving 0.5 + x2 = 9.394147114 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 = 9.394147114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 9.394147114 + -0.5 x2 = 9.394147114 + -0.5 Combine like terms: 9.394147114 + -0.5 = 8.894147114 x2 = 8.894147114 Simplifying x2 = 8.894147114 Take the square root of each side: x = {-2.982305671, 2.982305671}Subproblem 2
x2 + 0.5 = -9.394147114 Simplifying x2 + 0.5 = -9.394147114 Reorder the terms: 0.5 + x2 = -9.394147114 Solving 0.5 + x2 = -9.394147114 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 = -9.394147114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -9.394147114 + -0.5 x2 = -9.394147114 + -0.5 Combine like terms: -9.394147114 + -0.5 = -9.894147114 x2 = -9.894147114 Simplifying x2 = -9.894147114 Reorder the terms: 9.894147114 + x2 = -9.894147114 + 9.894147114 Combine like terms: -9.894147114 + 9.894147114 = 0.000000000 9.894147114 + 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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