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Simplifying 2178 = 132y + -2y2 Solving 2178 = 132y + -2y2 Solving for variable 'y'. Reorder the terms: 2178 + -132y + 2y2 = 132y + -132y + -2y2 + 2y2 Combine like terms: 132y + -132y = 0 2178 + -132y + 2y2 = 0 + -2y2 + 2y2 2178 + -132y + 2y2 = -2y2 + 2y2 Combine like terms: -2y2 + 2y2 = 0 2178 + -132y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1089 + -66y + y2) = 0 Factor a trinomial. 2((33 + -1y)(33 + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(33 + -1y)' equal to zero and attempt to solve: Simplifying 33 + -1y = 0 Solving 33 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1y = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1y = 0 + -33 -1y = 0 + -33 Combine like terms: 0 + -33 = -33 -1y = -33 Divide each side by '-1'. y = 33 Simplifying y = 33Subproblem 2
Set the factor '(33 + -1y)' equal to zero and attempt to solve: Simplifying 33 + -1y = 0 Solving 33 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-33' to each side of the equation. 33 + -33 + -1y = 0 + -33 Combine like terms: 33 + -33 = 0 0 + -1y = 0 + -33 -1y = 0 + -33 Combine like terms: 0 + -33 = -33 -1y = -33 Divide each side by '-1'. y = 33 Simplifying y = 33Solution
y = {33, 33}
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