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Simplifying x2(x2 + -64) + -81(x2 + -64) = 0 Reorder the terms: x2(-64 + x2) + -81(x2 + -64) = 0 (-64 * x2 + x2 * x2) + -81(x2 + -64) = 0 (-64x2 + x4) + -81(x2 + -64) = 0 Reorder the terms: -64x2 + x4 + -81(-64 + x2) = 0 -64x2 + x4 + (-64 * -81 + x2 * -81) = 0 -64x2 + x4 + (5184 + -81x2) = 0 Reorder the terms: 5184 + -64x2 + -81x2 + x4 = 0 Combine like terms: -64x2 + -81x2 = -145x2 5184 + -145x2 + x4 = 0 Solving 5184 + -145x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (64 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((8 + x)(8 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(8 + x)(8 + -1x) = 0Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Subproblem 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 = {-8, 8, -9, 9}
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