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Simplifying 2y2 + 5y + 31 + -1y2 + 10y + 25 = 0 Reorder the terms: 31 + 25 + 5y + 10y + 2y2 + -1y2 = 0 Combine like terms: 31 + 25 = 56 56 + 5y + 10y + 2y2 + -1y2 = 0 Combine like terms: 5y + 10y = 15y 56 + 15y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 56 + 15y + 1y2 = 0 Solving 56 + 15y + 1y2 = 0 Solving for variable 'y'. Factor a trinomial. (8 + y)(7 + y) = 0Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve: Simplifying 8 + y = 0 Solving 8 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + y = 0 + -8 y = 0 + -8 Combine like terms: 0 + -8 = -8 y = -8 Simplifying y = -8Subproblem 2
Set the factor '(7 + y)' equal to zero and attempt to solve: Simplifying 7 + y = 0 Solving 7 + y = 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 + y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + y = 0 + -7 y = 0 + -7 Combine like terms: 0 + -7 = -7 y = -7 Simplifying y = -7Solution
y = {-8, -7}
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