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Simplifying x + 7 = x2 + 6x + 13 Reorder the terms: 7 + x = x2 + 6x + 13 Reorder the terms: 7 + x = 13 + 6x + x2 Solving 7 + x = 13 + 6x + x2 Solving for variable 'x'. Reorder the terms: 7 + -13 + x + -6x + -1x2 = 13 + 6x + x2 + -13 + -6x + -1x2 Combine like terms: 7 + -13 = -6 -6 + x + -6x + -1x2 = 13 + 6x + x2 + -13 + -6x + -1x2 Combine like terms: x + -6x = -5x -6 + -5x + -1x2 = 13 + 6x + x2 + -13 + -6x + -1x2 Reorder the terms: -6 + -5x + -1x2 = 13 + -13 + 6x + -6x + x2 + -1x2 Combine like terms: 13 + -13 = 0 -6 + -5x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -6 + -5x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -6 + -5x + -1x2 = 0 + x2 + -1x2 -6 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + -5x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5x + x2) = 0 Factor a trinomial. -1((3 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 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 = {-3, -2}
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