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Simplifying 0 = 4x2 + 59x + 172 Reorder the terms: 0 = 172 + 59x + 4x2 Solving 0 = 172 + 59x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -172 = -172 -172 + -59x + -4x2 = 172 + 59x + 4x2 + -172 + -59x + -4x2 Reorder the terms: -172 + -59x + -4x2 = 172 + -172 + 59x + -59x + 4x2 + -4x2 Combine like terms: 172 + -172 = 0 -172 + -59x + -4x2 = 0 + 59x + -59x + 4x2 + -4x2 -172 + -59x + -4x2 = 59x + -59x + 4x2 + -4x2 Combine like terms: 59x + -59x = 0 -172 + -59x + -4x2 = 0 + 4x2 + -4x2 -172 + -59x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -172 + -59x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(172 + 59x + 4x2) = 0 Factor a trinomial. -1((43 + 4x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(43 + 4x)' equal to zero and attempt to solve: Simplifying 43 + 4x = 0 Solving 43 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + 4x = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 4x = 0 + -43 4x = 0 + -43 Combine like terms: 0 + -43 = -43 4x = -43 Divide each side by '4'. x = -10.75 Simplifying x = -10.75Subproblem 2
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 = -4Solution
x = {-10.75, -4}
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