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Simplifying X4 + X2 = 20 Reorder the terms: X2 + X4 = 20 Solving X2 + X4 = 20 Solving for variable 'X'. Reorder the terms: -20 + X2 + X4 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + X2 + X4 = 0 Factor a trinomial. (-5 + -1X2)(4 + -1X2) = 0 Factor a difference between two squares. (-5 + -1X2)((2 + X)(2 + -1X)) = 0Subproblem 1
Set the factor '(-5 + -1X2)' equal to zero and attempt to solve: Simplifying -5 + -1X2 = 0 Solving -5 + -1X2 = 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 + -1X2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1X2 = 0 + 5 -1X2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1X2 = 5 Divide each side by '-1'. 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 '(2 + X)' equal to zero and attempt to solve: Simplifying 2 + X = 0 Solving 2 + X = 0 Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + X = 0 + -2 X = 0 + -2 Combine like terms: 0 + -2 = -2 X = -2 Simplifying X = -2Subproblem 3
Set the factor '(2 + -1X)' equal to zero and attempt to solve: Simplifying 2 + -1X = 0 Solving 2 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1X = 0 + -2 -1X = 0 + -2 Combine like terms: 0 + -2 = -2 -1X = -2 Divide each side by '-1'. X = 2 Simplifying X = 2Solution
X = {-2, 2}
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