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Simplifying x2(x2 + -25) + -81(x2 + -25) = 0 Reorder the terms: x2(-25 + x2) + -81(x2 + -25) = 0 (-25 * x2 + x2 * x2) + -81(x2 + -25) = 0 (-25x2 + x4) + -81(x2 + -25) = 0 Reorder the terms: -25x2 + x4 + -81(-25 + x2) = 0 -25x2 + x4 + (-25 * -81 + x2 * -81) = 0 -25x2 + x4 + (2025 + -81x2) = 0 Reorder the terms: 2025 + -25x2 + -81x2 + x4 = 0 Combine like terms: -25x2 + -81x2 = -106x2 2025 + -106x2 + x4 = 0 Solving 2025 + -106x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (25 + -1x2)(81 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -1x))(81 + -1x2) = 0 Factor a difference between two squares. ((9 + x)(9 + -1x))(5 + x)(5 + -1x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Subproblem 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 = {-5, 5, -9, 9}
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