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Simplifying x2(x2 + -1) + -81(x2 + -1) = 0 Reorder the terms: x2(-1 + x2) + -81(x2 + -1) = 0 (-1 * x2 + x2 * x2) + -81(x2 + -1) = 0 (-1x2 + x4) + -81(x2 + -1) = 0 Reorder the terms: -1x2 + x4 + -81(-1 + x2) = 0 -1x2 + x4 + (-1 * -81 + x2 * -81) = 0 -1x2 + x4 + (81 + -81x2) = 0 Reorder the terms: 81 + -1x2 + -81x2 + x4 = 0 Combine like terms: -1x2 + -81x2 = -82x2 81 + -82x2 + x4 = 0 Solving 81 + -82x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 3
Set the factor '(9 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Subproblem 4
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-1, 1, -9, 9}
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