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Simplifying x2(x2 + -16) + -9(x2 + -16) = 0 Reorder the terms: x2(-16 + x2) + -9(x2 + -16) = 0 (-16 * x2 + x2 * x2) + -9(x2 + -16) = 0 (-16x2 + x4) + -9(x2 + -16) = 0 Reorder the terms: -16x2 + x4 + -9(-16 + x2) = 0 -16x2 + x4 + (-16 * -9 + x2 * -9) = 0 -16x2 + x4 + (144 + -9x2) = 0 Reorder the terms: 144 + -16x2 + -9x2 + x4 = 0 Combine like terms: -16x2 + -9x2 = -25x2 144 + -25x2 + x4 = 0 Solving 144 + -25x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (9 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(3 + -1x))(16 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-3, 3, -4, 4}
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