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Simplifying 0 = x4 + -20x2 + -125 Reorder the terms: 0 = -125 + -20x2 + x4 Solving 0 = -125 + -20x2 + x4 Solving for variable 'x'. Combine like terms: 0 + 125 = 125 125 + 20x2 + -1x4 = -125 + -20x2 + x4 + 125 + 20x2 + -1x4 Reorder the terms: 125 + 20x2 + -1x4 = -125 + 125 + -20x2 + 20x2 + x4 + -1x4 Combine like terms: -125 + 125 = 0 125 + 20x2 + -1x4 = 0 + -20x2 + 20x2 + x4 + -1x4 125 + 20x2 + -1x4 = -20x2 + 20x2 + x4 + -1x4 Combine like terms: -20x2 + 20x2 = 0 125 + 20x2 + -1x4 = 0 + x4 + -1x4 125 + 20x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 125 + 20x2 + -1x4 = 0 Factor a trinomial. (25 + -1x2)(5 + x2) = 0 Factor a difference between two squares. ((5 + x)(5 + -1x))(5 + x2) = 0Subproblem 1
Set the factor '(5 + x2)' equal to zero and attempt to solve: Simplifying 5 + x2 = 0 Solving 5 + x2 = 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 + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x2 = 0 + -5 x2 = 0 + -5 Combine like terms: 0 + -5 = -5 x2 = -5 Simplifying x2 = -5 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.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 + -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 = {-5, 5}
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