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Simplifying 0 = 5x2 + 31x + 42 Reorder the terms: 0 = 42 + 31x + 5x2 Solving 0 = 42 + 31x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -42 = -42 -42 + -31x + -5x2 = 42 + 31x + 5x2 + -42 + -31x + -5x2 Reorder the terms: -42 + -31x + -5x2 = 42 + -42 + 31x + -31x + 5x2 + -5x2 Combine like terms: 42 + -42 = 0 -42 + -31x + -5x2 = 0 + 31x + -31x + 5x2 + -5x2 -42 + -31x + -5x2 = 31x + -31x + 5x2 + -5x2 Combine like terms: 31x + -31x = 0 -42 + -31x + -5x2 = 0 + 5x2 + -5x2 -42 + -31x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -42 + -31x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(42 + 31x + 5x2) = 0 Factor a trinomial. -1((21 + 5x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 5x)' equal to zero and attempt to solve: Simplifying 21 + 5x = 0 Solving 21 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 5x = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 5x = 0 + -21 5x = 0 + -21 Combine like terms: 0 + -21 = -21 5x = -21 Divide each side by '5'. x = -4.2 Simplifying x = -4.2Subproblem 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 = {-4.2, -2}
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