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Simplifying 2Y + 9Y(Y + -4) = 52 Reorder the terms: 2Y + 9Y(-4 + Y) = 52 2Y + (-4 * 9Y + Y * 9Y) = 52 2Y + (-36Y + 9Y2) = 52 Combine like terms: 2Y + -36Y = -34Y -34Y + 9Y2 = 52 Solving -34Y + 9Y2 = 52 Solving for variable 'Y'. Reorder the terms: -52 + -34Y + 9Y2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + -34Y + 9Y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5.777777778 + -3.777777778Y + Y2 = 0 Move the constant term to the right: Add '5.777777778' to each side of the equation. -5.777777778 + -3.777777778Y + 5.777777778 + Y2 = 0 + 5.777777778 Reorder the terms: -5.777777778 + 5.777777778 + -3.777777778Y + Y2 = 0 + 5.777777778 Combine like terms: -5.777777778 + 5.777777778 = 0.000000000 0.000000000 + -3.777777778Y + Y2 = 0 + 5.777777778 -3.777777778Y + Y2 = 0 + 5.777777778 Combine like terms: 0 + 5.777777778 = 5.777777778 -3.777777778Y + Y2 = 5.777777778 The Y term is -3.777777778Y. Take half its coefficient (-1.888888889). Square it (3.567901235) and add it to both sides. Add '3.567901235' to each side of the equation. -3.777777778Y + 3.567901235 + Y2 = 5.777777778 + 3.567901235 Reorder the terms: 3.567901235 + -3.777777778Y + Y2 = 5.777777778 + 3.567901235 Combine like terms: 5.777777778 + 3.567901235 = 9.345679013 3.567901235 + -3.777777778Y + Y2 = 9.345679013 Factor a perfect square on the left side: (Y + -1.888888889)(Y + -1.888888889) = 9.345679013 Calculate the square root of the right side: 3.057070332 Break this problem into two subproblems by setting (Y + -1.888888889) equal to 3.057070332 and -3.057070332.Subproblem 1
Y + -1.888888889 = 3.057070332 Simplifying Y + -1.888888889 = 3.057070332 Reorder the terms: -1.888888889 + Y = 3.057070332 Solving -1.888888889 + Y = 3.057070332 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + Y = 3.057070332 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + Y = 3.057070332 + 1.888888889 Y = 3.057070332 + 1.888888889 Combine like terms: 3.057070332 + 1.888888889 = 4.945959221 Y = 4.945959221 Simplifying Y = 4.945959221Subproblem 2
Y + -1.888888889 = -3.057070332 Simplifying Y + -1.888888889 = -3.057070332 Reorder the terms: -1.888888889 + Y = -3.057070332 Solving -1.888888889 + Y = -3.057070332 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '1.888888889' to each side of the equation. -1.888888889 + 1.888888889 + Y = -3.057070332 + 1.888888889 Combine like terms: -1.888888889 + 1.888888889 = 0.000000000 0.000000000 + Y = -3.057070332 + 1.888888889 Y = -3.057070332 + 1.888888889 Combine like terms: -3.057070332 + 1.888888889 = -1.168181443 Y = -1.168181443 Simplifying Y = -1.168181443Solution
The solution to the problem is based on the solutions from the subproblems. Y = {4.945959221, -1.168181443}
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