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Simplifying 4x4 = 13x2 + -9 Reorder the terms: 4x4 = -9 + 13x2 Solving 4x4 = -9 + 13x2 Solving for variable 'x'. Reorder the terms: 9 + -13x2 + 4x4 = -9 + 13x2 + 9 + -13x2 Reorder the terms: 9 + -13x2 + 4x4 = -9 + 9 + 13x2 + -13x2 Combine like terms: -9 + 9 = 0 9 + -13x2 + 4x4 = 0 + 13x2 + -13x2 9 + -13x2 + 4x4 = 13x2 + -13x2 Combine like terms: 13x2 + -13x2 = 0 9 + -13x2 + 4x4 = 0 Factor a trinomial. (1 + -1x2)(9 + -4x2) = 0 Factor a difference between two squares. ((1 + x)(1 + -1x))(9 + -4x2) = 0 Factor a difference between two squares. ((3 + 2x)(3 + -2x))(1 + x)(1 + -1x) = 0Subproblem 1
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 2
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 = 1Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 4
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {-1, 1, -1.5, 1.5}
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