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Simplifying 0 = 34y + -1y2 + -120 Reorder the terms: 0 = -120 + 34y + -1y2 Solving 0 = -120 + 34y + -1y2 Solving for variable 'y'. Combine like terms: 0 + 120 = 120 120 + -34y + y2 = -120 + 34y + -1y2 + 120 + -34y + y2 Reorder the terms: 120 + -34y + y2 = -120 + 120 + 34y + -34y + -1y2 + y2 Combine like terms: -120 + 120 = 0 120 + -34y + y2 = 0 + 34y + -34y + -1y2 + y2 120 + -34y + y2 = 34y + -34y + -1y2 + y2 Combine like terms: 34y + -34y = 0 120 + -34y + y2 = 0 + -1y2 + y2 120 + -34y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 120 + -34y + y2 = 0 Factor a trinomial. (4 + -1y)(30 + -1y) = 0Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4Subproblem 2
Set the factor '(30 + -1y)' equal to zero and attempt to solve: Simplifying 30 + -1y = 0 Solving 30 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1y = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1y = 0 + -30 -1y = 0 + -30 Combine like terms: 0 + -30 = -30 -1y = -30 Divide each side by '-1'. y = 30 Simplifying y = 30Solution
y = {4, 30}
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