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Simplifying x2(x2 + -16) + -25(x2 + -16) = 0 Reorder the terms: x2(-16 + x2) + -25(x2 + -16) = 0 (-16 * x2 + x2 * x2) + -25(x2 + -16) = 0 (-16x2 + x4) + -25(x2 + -16) = 0 Reorder the terms: -16x2 + x4 + -25(-16 + x2) = 0 -16x2 + x4 + (-16 * -25 + x2 * -25) = 0 -16x2 + x4 + (400 + -25x2) = 0 Reorder the terms: 400 + -16x2 + -25x2 + x4 = 0 Combine like terms: -16x2 + -25x2 = -41x2 400 + -41x2 + x4 = 0 Solving 400 + -41x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (16 + -1x2)(25 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(25 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -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 '(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 4
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 = 5Solution
x = {-4, 4, -5, 5}
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