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Simplifying -2x2 + 78x + 60 = 600 Reorder the terms: 60 + 78x + -2x2 = 600 Solving 60 + 78x + -2x2 = 600 Solving for variable 'x'. Reorder the terms: 60 + -600 + 78x + -2x2 = 600 + -600 Combine like terms: 60 + -600 = -540 -540 + 78x + -2x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -540 + 78x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-270 + 39x + -1x2) = 0 Factor a trinomial. 2((-30 + x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + x)' equal to zero and attempt to solve: Simplifying -30 + x = 0 Solving -30 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 0 + 30 Combine like terms: -30 + 30 = 0 0 + x = 0 + 30 x = 0 + 30 Combine like terms: 0 + 30 = 30 x = 30 Simplifying x = 30Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {30, 9}
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