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Simplifying 32y + 112 = y2 + 22y + 121 Reorder the terms: 112 + 32y = y2 + 22y + 121 Reorder the terms: 112 + 32y = 121 + 22y + y2 Solving 112 + 32y = 121 + 22y + y2 Solving for variable 'y'. Reorder the terms: 112 + -121 + 32y + -22y + -1y2 = 121 + 22y + y2 + -121 + -22y + -1y2 Combine like terms: 112 + -121 = -9 -9 + 32y + -22y + -1y2 = 121 + 22y + y2 + -121 + -22y + -1y2 Combine like terms: 32y + -22y = 10y -9 + 10y + -1y2 = 121 + 22y + y2 + -121 + -22y + -1y2 Reorder the terms: -9 + 10y + -1y2 = 121 + -121 + 22y + -22y + y2 + -1y2 Combine like terms: 121 + -121 = 0 -9 + 10y + -1y2 = 0 + 22y + -22y + y2 + -1y2 -9 + 10y + -1y2 = 22y + -22y + y2 + -1y2 Combine like terms: 22y + -22y = 0 -9 + 10y + -1y2 = 0 + y2 + -1y2 -9 + 10y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -9 + 10y + -1y2 = 0 Factor a trinomial. (-9 + y)(1 + -1y) = 0Subproblem 1
Set the factor '(-9 + y)' equal to zero and attempt to solve: Simplifying -9 + y = 0 Solving -9 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 0 + 9 Combine like terms: -9 + 9 = 0 0 + y = 0 + 9 y = 0 + 9 Combine like terms: 0 + 9 = 9 y = 9 Simplifying y = 9Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 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 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Solution
y = {9, 1}
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