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Simplifying x2(x2 + -64) + -25(x2 + -64) = 0 Reorder the terms: x2(-64 + x2) + -25(x2 + -64) = 0 (-64 * x2 + x2 * x2) + -25(x2 + -64) = 0 (-64x2 + x4) + -25(x2 + -64) = 0 Reorder the terms: -64x2 + x4 + -25(-64 + x2) = 0 -64x2 + x4 + (-64 * -25 + x2 * -25) = 0 -64x2 + x4 + (1600 + -25x2) = 0 Reorder the terms: 1600 + -64x2 + -25x2 + x4 = 0 Combine like terms: -64x2 + -25x2 = -89x2 1600 + -89x2 + x4 = 0 Solving 1600 + -89x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (25 + -1x2)(64 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -1x))(64 + -1x2) = 0 Factor a difference between two squares. ((8 + x)(8 + -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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 4
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-5, 5, -8, 8}
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