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Simplifying 0 = 4x2 + 31x + 60 Reorder the terms: 0 = 60 + 31x + 4x2 Solving 0 = 60 + 31x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -31x + -4x2 = 60 + 31x + 4x2 + -60 + -31x + -4x2 Reorder the terms: -60 + -31x + -4x2 = 60 + -60 + 31x + -31x + 4x2 + -4x2 Combine like terms: 60 + -60 = 0 -60 + -31x + -4x2 = 0 + 31x + -31x + 4x2 + -4x2 -60 + -31x + -4x2 = 31x + -31x + 4x2 + -4x2 Combine like terms: 31x + -31x = 0 -60 + -31x + -4x2 = 0 + 4x2 + -4x2 -60 + -31x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -60 + -31x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 31x + 4x2) = 0 Factor a trinomial. -1((4 + x)(15 + 4x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(15 + 4x)' equal to zero and attempt to solve: Simplifying 15 + 4x = 0 Solving 15 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 4x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 4x = 0 + -15 4x = 0 + -15 Combine like terms: 0 + -15 = -15 4x = -15 Divide each side by '4'. x = -3.75 Simplifying x = -3.75Solution
x = {-4, -3.75}
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