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Simplifying 0 = 2x2 + 30x + 52 Reorder the terms: 0 = 52 + 30x + 2x2 Solving 0 = 52 + 30x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -52 = -52 -52 + -30x + -2x2 = 52 + 30x + 2x2 + -52 + -30x + -2x2 Reorder the terms: -52 + -30x + -2x2 = 52 + -52 + 30x + -30x + 2x2 + -2x2 Combine like terms: 52 + -52 = 0 -52 + -30x + -2x2 = 0 + 30x + -30x + 2x2 + -2x2 -52 + -30x + -2x2 = 30x + -30x + 2x2 + -2x2 Combine like terms: 30x + -30x = 0 -52 + -30x + -2x2 = 0 + 2x2 + -2x2 -52 + -30x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -52 + -30x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(26 + 15x + x2) = 0 Factor a trinomial. -2((13 + x)(2 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Simplifying x = -13Subproblem 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 = {-13, -2}
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