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Simplifying x2(x2 + -9) + -36(x2 + -9) = 0 Reorder the terms: x2(-9 + x2) + -36(x2 + -9) = 0 (-9 * x2 + x2 * x2) + -36(x2 + -9) = 0 (-9x2 + x4) + -36(x2 + -9) = 0 Reorder the terms: -9x2 + x4 + -36(-9 + x2) = 0 -9x2 + x4 + (-9 * -36 + x2 * -36) = 0 -9x2 + x4 + (324 + -36x2) = 0 Reorder the terms: 324 + -9x2 + -36x2 + x4 = 0 Combine like terms: -9x2 + -36x2 = -45x2 324 + -45x2 + x4 = 0 Solving 324 + -45x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -1x2)(36 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(36 + -1x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(3 + x)(3 + -1x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 4
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-3, 3, -6, 6}
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