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Simplifying x2 + 12x + 13 = 5x + 3 Reorder the terms: 13 + 12x + x2 = 5x + 3 Reorder the terms: 13 + 12x + x2 = 3 + 5x Solving 13 + 12x + x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: 13 + -3 + 12x + -5x + x2 = 3 + 5x + -3 + -5x Combine like terms: 13 + -3 = 10 10 + 12x + -5x + x2 = 3 + 5x + -3 + -5x Combine like terms: 12x + -5x = 7x 10 + 7x + x2 = 3 + 5x + -3 + -5x Reorder the terms: 10 + 7x + x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 10 + 7x + x2 = 0 + 5x + -5x 10 + 7x + x2 = 5x + -5x Combine like terms: 5x + -5x = 0 10 + 7x + x2 = 0 Factor a trinomial. (5 + x)(2 + x) = 0Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-5, -2}
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