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Simplifying x2(x2 + -36) + -16(x2 + -36) = 0 Reorder the terms: x2(-36 + x2) + -16(x2 + -36) = 0 (-36 * x2 + x2 * x2) + -16(x2 + -36) = 0 (-36x2 + x4) + -16(x2 + -36) = 0 Reorder the terms: -36x2 + x4 + -16(-36 + x2) = 0 -36x2 + x4 + (-36 * -16 + x2 * -16) = 0 -36x2 + x4 + (576 + -16x2) = 0 Reorder the terms: 576 + -36x2 + -16x2 + x4 = 0 Combine like terms: -36x2 + -16x2 = -52x2 576 + -52x2 + x4 = 0 Solving 576 + -52x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (16 + -1x2)(36 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(36 + -1x2) = 0 Factor a difference between two squares. ((6 + x)(6 + -1x))(4 + x)(4 + -1x) = 0Subproblem 1
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 2
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 = 4Subproblem 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 = {-4, 4, -6, 6}
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