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Simplifying 10 = x2 + 11x + 40 Reorder the terms: 10 = 40 + 11x + x2 Solving 10 = 40 + 11x + x2 Solving for variable 'x'. Combine like terms: 10 + -40 = -30 -30 + -11x + -1x2 = 40 + 11x + x2 + -40 + -11x + -1x2 Reorder the terms: -30 + -11x + -1x2 = 40 + -40 + 11x + -11x + x2 + -1x2 Combine like terms: 40 + -40 = 0 -30 + -11x + -1x2 = 0 + 11x + -11x + x2 + -1x2 -30 + -11x + -1x2 = 11x + -11x + x2 + -1x2 Combine like terms: 11x + -11x = 0 -30 + -11x + -1x2 = 0 + x2 + -1x2 -30 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -30 + -11x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + 11x + x2) = 0 Factor a trinomial. -1((6 + x)(5 + x)) = 0 Ignore the factor -1.Subproblem 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 '(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 = -5Solution
x = {-6, -5}
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