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Simplifying 2y2 = 15 + y Solving 2y2 = 15 + y Solving for variable 'y'. Reorder the terms: -15 + -1y + 2y2 = 15 + y + -15 + -1y Reorder the terms: -15 + -1y + 2y2 = 15 + -15 + y + -1y Combine like terms: 15 + -15 = 0 -15 + -1y + 2y2 = 0 + y + -1y -15 + -1y + 2y2 = y + -1y Combine like terms: y + -1y = 0 -15 + -1y + 2y2 = 0 Factor a trinomial. (-5 + -2y)(3 + -1y) = 0Subproblem 1
Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve: Simplifying 3 + -1y = 0 Solving 3 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1y = 0 + -3 -1y = 0 + -3 Combine like terms: 0 + -3 = -3 -1y = -3 Divide each side by '-1'. y = 3 Simplifying y = 3Solution
y = {-2.5, 3}
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