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Simplifying -1x6 = 25x2 + -26x4 Solving -1x6 = 25x2 + -26x4 Solving for variable 'x'. Reorder the terms: -25x2 + 26x4 + -1x6 = 25x2 + -26x4 + -25x2 + 26x4 Reorder the terms: -25x2 + 26x4 + -1x6 = 25x2 + -25x2 + -26x4 + 26x4 Combine like terms: 25x2 + -25x2 = 0 -25x2 + 26x4 + -1x6 = 0 + -26x4 + 26x4 -25x2 + 26x4 + -1x6 = -26x4 + 26x4 Combine like terms: -26x4 + 26x4 = 0 -25x2 + 26x4 + -1x6 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-25 + 26x2 + -1x4) = 0 Factor a trinomial. x2((-25 + x2)(1 + -1x2)) = 0 Factor a difference between two squares. x2(((5 + x)(-5 + x))(1 + -1x2)) = 0 Factor a difference between two squares. x2(((1 + x)(1 + -1x))(5 + x)(-5 + x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 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 '(-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 '(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 5
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 = {0, -5, 5, -1, 1}
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