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Simplifying x2 + -13x + 22 = -4x + 4 Reorder the terms: 22 + -13x + x2 = -4x + 4 Reorder the terms: 22 + -13x + x2 = 4 + -4x Solving 22 + -13x + x2 = 4 + -4x Solving for variable 'x'. Reorder the terms: 22 + -4 + -13x + 4x + x2 = 4 + -4x + -4 + 4x Combine like terms: 22 + -4 = 18 18 + -13x + 4x + x2 = 4 + -4x + -4 + 4x Combine like terms: -13x + 4x = -9x 18 + -9x + x2 = 4 + -4x + -4 + 4x Reorder the terms: 18 + -9x + x2 = 4 + -4 + -4x + 4x Combine like terms: 4 + -4 = 0 18 + -9x + x2 = 0 + -4x + 4x 18 + -9x + x2 = -4x + 4x Combine like terms: -4x + 4x = 0 18 + -9x + x2 = 0 Factor a trinomial. (3 + -1x)(6 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {3, 6}
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