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Simplifying x2(x2 + -25) + -1(x2 + -25) = 0 Reorder the terms: x2(-25 + x2) + -1(x2 + -25) = 0 (-25 * x2 + x2 * x2) + -1(x2 + -25) = 0 (-25x2 + x4) + -1(x2 + -25) = 0 Reorder the terms: -25x2 + x4 + -1(-25 + x2) = 0 -25x2 + x4 + (-25 * -1 + x2 * -1) = 0 -25x2 + x4 + (25 + -1x2) = 0 Reorder the terms: 25 + -25x2 + -1x2 + x4 = 0 Combine like terms: -25x2 + -1x2 = -26x2 25 + -26x2 + x4 = 0 Solving 25 + -26x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -1x2)(25 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(25 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -1x))(1 + x)(1 + -1x) = 0Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 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 = {-1, 1, -5, 5}
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