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Simplifying 0 = 4x2 + 31x + 46 Reorder the terms: 0 = 46 + 31x + 4x2 Solving 0 = 46 + 31x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -46 = -46 -46 + -31x + -4x2 = 46 + 31x + 4x2 + -46 + -31x + -4x2 Reorder the terms: -46 + -31x + -4x2 = 46 + -46 + 31x + -31x + 4x2 + -4x2 Combine like terms: 46 + -46 = 0 -46 + -31x + -4x2 = 0 + 31x + -31x + 4x2 + -4x2 -46 + -31x + -4x2 = 31x + -31x + 4x2 + -4x2 Combine like terms: 31x + -31x = 0 -46 + -31x + -4x2 = 0 + 4x2 + -4x2 -46 + -31x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -46 + -31x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(46 + 31x + 4x2) = 0 Factor a trinomial. -1((23 + 4x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 4x)' equal to zero and attempt to solve: Simplifying 23 + 4x = 0 Solving 23 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 4x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 4x = 0 + -23 4x = 0 + -23 Combine like terms: 0 + -23 = -23 4x = -23 Divide each side by '4'. x = -5.75 Simplifying x = -5.75Subproblem 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 = {-5.75, -2}
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