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Simplifying 0 = 10x2 + 31x + 24 Reorder the terms: 0 = 24 + 31x + 10x2 Solving 0 = 24 + 31x + 10x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -31x + -10x2 = 24 + 31x + 10x2 + -24 + -31x + -10x2 Reorder the terms: -24 + -31x + -10x2 = 24 + -24 + 31x + -31x + 10x2 + -10x2 Combine like terms: 24 + -24 = 0 -24 + -31x + -10x2 = 0 + 31x + -31x + 10x2 + -10x2 -24 + -31x + -10x2 = 31x + -31x + 10x2 + -10x2 Combine like terms: 31x + -31x = 0 -24 + -31x + -10x2 = 0 + 10x2 + -10x2 -24 + -31x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -24 + -31x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 31x + 10x2) = 0 Factor a trinomial. -1((8 + 5x)(3 + 2x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 5x)' equal to zero and attempt to solve: Simplifying 8 + 5x = 0 Solving 8 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5x = 0 + -8 5x = 0 + -8 Combine like terms: 0 + -8 = -8 5x = -8 Divide each side by '5'. x = -1.6 Simplifying x = -1.6Subproblem 2
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 = -1.5Solution
x = {-1.6, -1.5}
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