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Simplifying x2 + -6x + 14 = 3x + -4 Reorder the terms: 14 + -6x + x2 = 3x + -4 Reorder the terms: 14 + -6x + x2 = -4 + 3x Solving 14 + -6x + x2 = -4 + 3x Solving for variable 'x'. Reorder the terms: 14 + 4 + -6x + -3x + x2 = -4 + 3x + 4 + -3x Combine like terms: 14 + 4 = 18 18 + -6x + -3x + x2 = -4 + 3x + 4 + -3x Combine like terms: -6x + -3x = -9x 18 + -9x + x2 = -4 + 3x + 4 + -3x Reorder the terms: 18 + -9x + x2 = -4 + 4 + 3x + -3x Combine like terms: -4 + 4 = 0 18 + -9x + x2 = 0 + 3x + -3x 18 + -9x + x2 = 3x + -3x Combine like terms: 3x + -3x = 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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