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Simplifying x4 + 2x2 + -125 = 0 Reorder the terms: -125 + 2x2 + x4 = 0 Solving -125 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 2x2 + 125 + x4 = 0 + 125 Reorder the terms: -125 + 125 + 2x2 + x4 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 2x2 + x4 = 0 + 125 2x2 + x4 = 0 + 125 Combine like terms: 0 + 125 = 125 2x2 + x4 = 125 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 125 + 1 Reorder the terms: 1 + 2x2 + x4 = 125 + 1 Combine like terms: 125 + 1 = 126 1 + 2x2 + x4 = 126 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (x2 + 1) equal to 11.22497216 and -11.22497216.Subproblem 1
x2 + 1 = 11.22497216 Simplifying x2 + 1 = 11.22497216 Reorder the terms: 1 + x2 = 11.22497216 Solving 1 + x2 = 11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 11.22497216 + -1 x2 = 11.22497216 + -1 Combine like terms: 11.22497216 + -1 = 10.22497216 x2 = 10.22497216 Simplifying x2 = 10.22497216 Take the square root of each side: x = {-3.197651038, 3.197651038}Subproblem 2
x2 + 1 = -11.22497216 Simplifying x2 + 1 = -11.22497216 Reorder the terms: 1 + x2 = -11.22497216 Solving 1 + x2 = -11.22497216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -11.22497216 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -11.22497216 + -1 x2 = -11.22497216 + -1 Combine like terms: -11.22497216 + -1 = -12.22497216 x2 = -12.22497216 Simplifying x2 = -12.22497216 Reorder the terms: 12.22497216 + x2 = -12.22497216 + 12.22497216 Combine like terms: -12.22497216 + 12.22497216 = 0.00000000 12.22497216 + x2 = 0.00000000 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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