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Simplifying 0 = 6(3x2 + -155x + -1500) Reorder the terms: 0 = 6(-1500 + -155x + 3x2) 0 = (-1500 * 6 + -155x * 6 + 3x2 * 6) 0 = (-9000 + -930x + 18x2) Solving 0 = -9000 + -930x + 18x2 Solving for variable 'x'. Combine like terms: 0 + 9000 = 9000 9000 + 930x + -18x2 = -9000 + -930x + 18x2 + 9000 + 930x + -18x2 Reorder the terms: 9000 + 930x + -18x2 = -9000 + 9000 + -930x + 930x + 18x2 + -18x2 Combine like terms: -9000 + 9000 = 0 9000 + 930x + -18x2 = 0 + -930x + 930x + 18x2 + -18x2 9000 + 930x + -18x2 = -930x + 930x + 18x2 + -18x2 Combine like terms: -930x + 930x = 0 9000 + 930x + -18x2 = 0 + 18x2 + -18x2 9000 + 930x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 9000 + 930x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(1500 + 155x + -3x2) = 0 Factor a trinomial. 6((60 + -1x)(25 + 3x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(60 + -1x)' equal to zero and attempt to solve: Simplifying 60 + -1x = 0 Solving 60 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-60' to each side of the equation. 60 + -60 + -1x = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -1x = 0 + -60 -1x = 0 + -60 Combine like terms: 0 + -60 = -60 -1x = -60 Divide each side by '-1'. x = 60 Simplifying x = 60Subproblem 2
Set the factor '(25 + 3x)' equal to zero and attempt to solve: Simplifying 25 + 3x = 0 Solving 25 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + 3x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 3x = 0 + -25 3x = 0 + -25 Combine like terms: 0 + -25 = -25 3x = -25 Divide each side by '3'. x = -8.333333333 Simplifying x = -8.333333333Solution
x = {60, -8.333333333}
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