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Simplifying 0 = x2 + 13x + 22 Reorder the terms: 0 = 22 + 13x + x2 Solving 0 = 22 + 13x + x2 Solving for variable 'x'. Combine like terms: 0 + -22 = -22 -22 + -13x + -1x2 = 22 + 13x + x2 + -22 + -13x + -1x2 Reorder the terms: -22 + -13x + -1x2 = 22 + -22 + 13x + -13x + x2 + -1x2 Combine like terms: 22 + -22 = 0 -22 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2 -22 + -13x + -1x2 = 13x + -13x + x2 + -1x2 Combine like terms: 13x + -13x = 0 -22 + -13x + -1x2 = 0 + x2 + -1x2 -22 + -13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -22 + -13x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(22 + 13x + x2) = 0 Factor a trinomial. -1((11 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve: Simplifying 11 + x = 0 Solving 11 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + x = 0 + -11 x = 0 + -11 Combine like terms: 0 + -11 = -11 x = -11 Simplifying x = -11Subproblem 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 = {-11, -2}
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