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Simplifying 12x2 + 34x = -24 Reorder the terms: 34x + 12x2 = -24 Solving 34x + 12x2 = -24 Solving for variable 'x'. Reorder the terms: 24 + 34x + 12x2 = -24 + 24 Combine like terms: -24 + 24 = 0 24 + 34x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 17x + 6x2) = 0 Factor a trinomial. 2((3 + 2x)(4 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {-1.5, -1.333333333}
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