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Simplifying x4 + -2x2 + -81 = 0 Reorder the terms: -81 + -2x2 + x4 = 0 Solving -81 + -2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + -2x2 + 81 + x4 = 0 + 81 Reorder the terms: -81 + 81 + -2x2 + x4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -2x2 + x4 = 0 + 81 -2x2 + x4 = 0 + 81 Combine like terms: 0 + 81 = 81 -2x2 + x4 = 81 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 = 81 + 1 Reorder the terms: 1 + -2x2 + x4 = 81 + 1 Combine like terms: 81 + 1 = 82 1 + -2x2 + x4 = 82 Factor a perfect square on the left side: (x2 + -1)(x2 + -1) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x2 + -1) equal to 9.055385138 and -9.055385138.Subproblem 1
x2 + -1 = 9.055385138 Simplifying x2 + -1 = 9.055385138 Reorder the terms: -1 + x2 = 9.055385138 Solving -1 + x2 = 9.055385138 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 = 9.055385138 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = 9.055385138 + 1 x2 = 9.055385138 + 1 Combine like terms: 9.055385138 + 1 = 10.055385138 x2 = 10.055385138 Simplifying x2 = 10.055385138 Take the square root of each side: x = {-3.171022727, 3.171022727}Subproblem 2
x2 + -1 = -9.055385138 Simplifying x2 + -1 = -9.055385138 Reorder the terms: -1 + x2 = -9.055385138 Solving -1 + x2 = -9.055385138 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 = -9.055385138 + 1 Combine like terms: -1 + 1 = 0 0 + x2 = -9.055385138 + 1 x2 = -9.055385138 + 1 Combine like terms: -9.055385138 + 1 = -8.055385138 x2 = -8.055385138 Simplifying x2 = -8.055385138 Reorder the terms: 8.055385138 + x2 = -8.055385138 + 8.055385138 Combine like terms: -8.055385138 + 8.055385138 = 0.000000000 8.055385138 + 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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