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Simplifying 9y2 + -15y + -5 = y + 9 Reorder the terms: -5 + -15y + 9y2 = y + 9 Reorder the terms: -5 + -15y + 9y2 = 9 + y Solving -5 + -15y + 9y2 = 9 + y Solving for variable 'y'. Reorder the terms: -5 + -9 + -15y + -1y + 9y2 = 9 + y + -9 + -1y Combine like terms: -5 + -9 = -14 -14 + -15y + -1y + 9y2 = 9 + y + -9 + -1y Combine like terms: -15y + -1y = -16y -14 + -16y + 9y2 = 9 + y + -9 + -1y Reorder the terms: -14 + -16y + 9y2 = 9 + -9 + y + -1y Combine like terms: 9 + -9 = 0 -14 + -16y + 9y2 = 0 + y + -1y -14 + -16y + 9y2 = y + -1y Combine like terms: y + -1y = 0 -14 + -16y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + -1.777777778y + y2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + -1.777777778y + 1.555555556 + y2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + -1.777777778y + y2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + -1.777777778y + y2 = 0 + 1.555555556 -1.777777778y + y2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 -1.777777778y + y2 = 1.555555556 The y term is -1.777777778y. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778y + 0.7901234570 + y2 = 1.555555556 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778y + y2 = 1.555555556 + 0.7901234570 Combine like terms: 1.555555556 + 0.7901234570 = 2.345679013 0.7901234570 + -1.777777778y + y2 = 2.345679013 Factor a perfect square on the left side: (y + -0.888888889)(y + -0.888888889) = 2.345679013 Calculate the square root of the right side: 1.531560973 Break this problem into two subproblems by setting (y + -0.888888889) equal to 1.531560973 and -1.531560973.Subproblem 1
y + -0.888888889 = 1.531560973 Simplifying y + -0.888888889 = 1.531560973 Reorder the terms: -0.888888889 + y = 1.531560973 Solving -0.888888889 + y = 1.531560973 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + y = 1.531560973 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = 1.531560973 + 0.888888889 y = 1.531560973 + 0.888888889 Combine like terms: 1.531560973 + 0.888888889 = 2.420449862 y = 2.420449862 Simplifying y = 2.420449862Subproblem 2
y + -0.888888889 = -1.531560973 Simplifying y + -0.888888889 = -1.531560973 Reorder the terms: -0.888888889 + y = -1.531560973 Solving -0.888888889 + y = -1.531560973 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + y = -1.531560973 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = -1.531560973 + 0.888888889 y = -1.531560973 + 0.888888889 Combine like terms: -1.531560973 + 0.888888889 = -0.642672084 y = -0.642672084 Simplifying y = -0.642672084Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.420449862, -0.642672084}
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