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Simplifying 2Y2 = 13Y + 7 Reorder the terms: 2Y2 = 7 + 13Y Solving 2Y2 = 7 + 13Y Solving for variable 'Y'. Reorder the terms: -7 + -13Y + 2Y2 = 7 + 13Y + -7 + -13Y Reorder the terms: -7 + -13Y + 2Y2 = 7 + -7 + 13Y + -13Y Combine like terms: 7 + -7 = 0 -7 + -13Y + 2Y2 = 0 + 13Y + -13Y -7 + -13Y + 2Y2 = 13Y + -13Y Combine like terms: 13Y + -13Y = 0 -7 + -13Y + 2Y2 = 0 Factor a trinomial. (-1 + -2Y)(7 + -1Y) = 0Subproblem 1
Set the factor '(-1 + -2Y)' equal to zero and attempt to solve: Simplifying -1 + -2Y = 0 Solving -1 + -2Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2Y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2Y = 0 + 1 -2Y = 0 + 1 Combine like terms: 0 + 1 = 1 -2Y = 1 Divide each side by '-2'. Y = -0.5 Simplifying Y = -0.5Subproblem 2
Set the factor '(7 + -1Y)' equal to zero and attempt to solve: Simplifying 7 + -1Y = 0 Solving 7 + -1Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Y = 0 + -7 -1Y = 0 + -7 Combine like terms: 0 + -7 = -7 -1Y = -7 Divide each side by '-1'. Y = 7 Simplifying Y = 7Solution
Y = {-0.5, 7}
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