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Simplifying 42080 = -49x2 + 4606x + -52000 Reorder the terms: 42080 = -52000 + 4606x + -49x2 Solving 42080 = -52000 + 4606x + -49x2 Solving for variable 'x'. Combine like terms: 42080 + 52000 = 94080 94080 + -4606x + 49x2 = -52000 + 4606x + -49x2 + 52000 + -4606x + 49x2 Reorder the terms: 94080 + -4606x + 49x2 = -52000 + 52000 + 4606x + -4606x + -49x2 + 49x2 Combine like terms: -52000 + 52000 = 0 94080 + -4606x + 49x2 = 0 + 4606x + -4606x + -49x2 + 49x2 94080 + -4606x + 49x2 = 4606x + -4606x + -49x2 + 49x2 Combine like terms: 4606x + -4606x = 0 94080 + -4606x + 49x2 = 0 + -49x2 + 49x2 94080 + -4606x + 49x2 = -49x2 + 49x2 Combine like terms: -49x2 + 49x2 = 0 94080 + -4606x + 49x2 = 0 Factor out the Greatest Common Factor (GCF), '49'. 49(1920 + -94x + x2) = 0 Factor a trinomial. 49((30 + -1x)(64 + -1x)) = 0 Ignore the factor 49.Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 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 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
Set the factor '(64 + -1x)' equal to zero and attempt to solve: Simplifying 64 + -1x = 0 Solving 64 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-64' to each side of the equation. 64 + -64 + -1x = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -1x = 0 + -64 -1x = 0 + -64 Combine like terms: 0 + -64 = -64 -1x = -64 Divide each side by '-1'. x = 64 Simplifying x = 64Solution
x = {30, 64}
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