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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 + x2) = 0 Factor a trinomial. -2((30 + x)(9 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 9 + x = 0 Solving 9 + x = 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 + x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + x = 0 + -9 x = 0 + -9 Combine like terms: 0 + -9 = -9 x = -9 Simplifying x = -9Solution
x = {-30, -9}
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