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Simplifying x2(x2 + -4) + -81(x2 + -4) = 0 Reorder the terms: x2(-4 + x2) + -81(x2 + -4) = 0 (-4 * x2 + x2 * x2) + -81(x2 + -4) = 0 (-4x2 + x4) + -81(x2 + -4) = 0 Reorder the terms: -4x2 + x4 + -81(-4 + x2) = 0 -4x2 + x4 + (-4 * -81 + x2 * -81) = 0 -4x2 + x4 + (324 + -81x2) = 0 Reorder the terms: 324 + -4x2 + -81x2 + x4 = 0 Combine like terms: -4x2 + -81x2 = -85x2 324 + -85x2 + x4 = 0 Solving 324 + -85x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (4 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(2 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = {-2, 2, -9, 9}
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