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Simplifying x2 + 13x + 23 = 3x + -1 Reorder the terms: 23 + 13x + x2 = 3x + -1 Reorder the terms: 23 + 13x + x2 = -1 + 3x Solving 23 + 13x + x2 = -1 + 3x Solving for variable 'x'. Reorder the terms: 23 + 1 + 13x + -3x + x2 = -1 + 3x + 1 + -3x Combine like terms: 23 + 1 = 24 24 + 13x + -3x + x2 = -1 + 3x + 1 + -3x Combine like terms: 13x + -3x = 10x 24 + 10x + x2 = -1 + 3x + 1 + -3x Reorder the terms: 24 + 10x + x2 = -1 + 1 + 3x + -3x Combine like terms: -1 + 1 = 0 24 + 10x + x2 = 0 + 3x + -3x 24 + 10x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 24 + 10x + x2 = 0 Factor a trinomial. (6 + x)(4 + x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 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 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-6, -4}
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