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Simplifying 0 = 4x2 + 340x + 3000 Reorder the terms: 0 = 3000 + 340x + 4x2 Solving 0 = 3000 + 340x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -3000 = -3000 -3000 + -340x + -4x2 = 3000 + 340x + 4x2 + -3000 + -340x + -4x2 Reorder the terms: -3000 + -340x + -4x2 = 3000 + -3000 + 340x + -340x + 4x2 + -4x2 Combine like terms: 3000 + -3000 = 0 -3000 + -340x + -4x2 = 0 + 340x + -340x + 4x2 + -4x2 -3000 + -340x + -4x2 = 340x + -340x + 4x2 + -4x2 Combine like terms: 340x + -340x = 0 -3000 + -340x + -4x2 = 0 + 4x2 + -4x2 -3000 + -340x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3000 + -340x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(750 + 85x + x2) = 0 Factor a trinomial. -4((75 + x)(10 + x)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(75 + x)' equal to zero and attempt to solve: Simplifying 75 + x = 0 Solving 75 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + x = 0 + -75 Combine like terms: 75 + -75 = 0 0 + x = 0 + -75 x = 0 + -75 Combine like terms: 0 + -75 = -75 x = -75 Simplifying x = -75Subproblem 2
Set the factor '(10 + x)' equal to zero and attempt to solve: Simplifying 10 + x = 0 Solving 10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + x = 0 + -10 x = 0 + -10 Combine like terms: 0 + -10 = -10 x = -10 Simplifying x = -10Solution
x = {-75, -10}
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