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Simplifying x4 + 2x2 + -162 = 0 Reorder the terms: -162 + 2x2 + x4 = 0 Solving -162 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + 2x2 + 162 + x4 = 0 + 162 Reorder the terms: -162 + 162 + 2x2 + x4 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + 2x2 + x4 = 0 + 162 2x2 + x4 = 0 + 162 Combine like terms: 0 + 162 = 162 2x2 + x4 = 162 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 = 162 + 1 Reorder the terms: 1 + 2x2 + x4 = 162 + 1 Combine like terms: 162 + 1 = 163 1 + 2x2 + x4 = 163 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x2 + 1) equal to 12.767145335 and -12.767145335.Subproblem 1
x2 + 1 = 12.767145335 Simplifying x2 + 1 = 12.767145335 Reorder the terms: 1 + x2 = 12.767145335 Solving 1 + x2 = 12.767145335 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 = 12.767145335 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 12.767145335 + -1 x2 = 12.767145335 + -1 Combine like terms: 12.767145335 + -1 = 11.767145335 x2 = 11.767145335 Simplifying x2 = 11.767145335 Take the square root of each side: x = {-3.430327293, 3.430327293}Subproblem 2
x2 + 1 = -12.767145335 Simplifying x2 + 1 = -12.767145335 Reorder the terms: 1 + x2 = -12.767145335 Solving 1 + x2 = -12.767145335 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 = -12.767145335 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -12.767145335 + -1 x2 = -12.767145335 + -1 Combine like terms: -12.767145335 + -1 = -13.767145335 x2 = -13.767145335 Simplifying x2 = -13.767145335 Reorder the terms: 13.767145335 + x2 = -13.767145335 + 13.767145335 Combine like terms: -13.767145335 + 13.767145335 = 0.000000000 13.767145335 + 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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