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Simplifying 0 = x4 + -10x2 + 9 Reorder the terms: 0 = 9 + -10x2 + x4 Solving 0 = 9 + -10x2 + x4 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + 10x2 + -1x4 = 9 + -10x2 + x4 + -9 + 10x2 + -1x4 Reorder the terms: -9 + 10x2 + -1x4 = 9 + -9 + -10x2 + 10x2 + x4 + -1x4 Combine like terms: 9 + -9 = 0 -9 + 10x2 + -1x4 = 0 + -10x2 + 10x2 + x4 + -1x4 -9 + 10x2 + -1x4 = -10x2 + 10x2 + x4 + -1x4 Combine like terms: -10x2 + 10x2 = 0 -9 + 10x2 + -1x4 = 0 + x4 + -1x4 -9 + 10x2 + -1x4 = x4 + -1x4 Combine like terms: x4 + -1x4 = 0 -9 + 10x2 + -1x4 = 0 Factor a trinomial. (-9 + x2)(1 + -1x2) = 0 Factor a difference between two squares. ((3 + x)(-3 + x))(1 + -1x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(3 + x)(-3 + x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Simplifying x = 3Subproblem 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 = {-3, 3, -1, 1}
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