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Simplifying x4 + -16x2 + -81 = 0 Reorder the terms: -81 + -16x2 + x4 = 0 Solving -81 + -16x2 + 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 + -16x2 + 81 + x4 = 0 + 81 Reorder the terms: -81 + 81 + -16x2 + x4 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + -16x2 + x4 = 0 + 81 -16x2 + x4 = 0 + 81 Combine like terms: 0 + 81 = 81 -16x2 + x4 = 81 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = 81 + 64 Reorder the terms: 64 + -16x2 + x4 = 81 + 64 Combine like terms: 81 + 64 = 145 64 + -16x2 + x4 = 145 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x2 + -8) equal to 12.041594579 and -12.041594579.Subproblem 1
x2 + -8 = 12.041594579 Simplifying x2 + -8 = 12.041594579 Reorder the terms: -8 + x2 = 12.041594579 Solving -8 + x2 = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 12.041594579 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 12.041594579 + 8 x2 = 12.041594579 + 8 Combine like terms: 12.041594579 + 8 = 20.041594579 x2 = 20.041594579 Simplifying x2 = 20.041594579 Take the square root of each side: x = {-4.476783955, 4.476783955}Subproblem 2
x2 + -8 = -12.041594579 Simplifying x2 + -8 = -12.041594579 Reorder the terms: -8 + x2 = -12.041594579 Solving -8 + x2 = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -12.041594579 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -12.041594579 + 8 x2 = -12.041594579 + 8 Combine like terms: -12.041594579 + 8 = -4.041594579 x2 = -4.041594579 Simplifying x2 = -4.041594579 Reorder the terms: 4.041594579 + x2 = -4.041594579 + 4.041594579 Combine like terms: -4.041594579 + 4.041594579 = 0.000000000 4.041594579 + 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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