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Simplifying 0 = x4 + -26x2 + 25 Reorder the terms: 0 = 25 + -26x2 + x4 Solving 0 = 25 + -26x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -25 = -25 -25 + 26x2 + -1x4 = 25 + -26x2 + x4 + -25 + 26x2 + -1x4 Reorder the terms: -25 + 26x2 + -1x4 = 25 + -25 + -26x2 + 26x2 + x4 + -1x4 Combine like terms: 25 + -25 = 0 -25 + 26x2 + -1x4 = 0 + -26x2 + 26x2 + x4 + -1x4 -25 + 26x2 + -1x4 = -26x2 + 26x2 + x4 + -1x4 Combine like terms: -26x2 + 26x2 = 0 -25 + 26x2 + -1x4 = 0 + x4 + -1x4 -25 + 26x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -25 + 26x2 + -1x4 = 0 Factor a trinomial. (-25 + x2)(1 + -1x2) = 0 Factor a difference between two squares. ((5 + x)(-5 + x))(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(5 + x)(-5 + x) = 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 + 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 3
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 4
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 = 1Solution
x = {-5, 5, -1, 1}
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