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Simplifying 9y2 + -16y + -10 = 0 Reorder the terms: -10 + -16y + 9y2 = 0 Solving -10 + -16y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -1.777777778y + y2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -1.777777778y + 1.111111111 + y2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -1.777777778y + y2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -1.777777778y + y2 = 0 + 1.111111111 -1.777777778y + y2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -1.777777778y + y2 = 1.111111111 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 = 1.111111111 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778y + y2 = 1.111111111 + 0.7901234570 Combine like terms: 1.111111111 + 0.7901234570 = 1.901234568 0.7901234570 + -1.777777778y + y2 = 1.901234568 Factor a perfect square on the left side: (y + -0.888888889)(y + -0.888888889) = 1.901234568 Calculate the square root of the right side: 1.378852627 Break this problem into two subproblems by setting (y + -0.888888889) equal to 1.378852627 and -1.378852627.Subproblem 1
y + -0.888888889 = 1.378852627 Simplifying y + -0.888888889 = 1.378852627 Reorder the terms: -0.888888889 + y = 1.378852627 Solving -0.888888889 + y = 1.378852627 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 = 1.378852627 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = 1.378852627 + 0.888888889 y = 1.378852627 + 0.888888889 Combine like terms: 1.378852627 + 0.888888889 = 2.267741516 y = 2.267741516 Simplifying y = 2.267741516Subproblem 2
y + -0.888888889 = -1.378852627 Simplifying y + -0.888888889 = -1.378852627 Reorder the terms: -0.888888889 + y = -1.378852627 Solving -0.888888889 + y = -1.378852627 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 = -1.378852627 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + y = -1.378852627 + 0.888888889 y = -1.378852627 + 0.888888889 Combine like terms: -1.378852627 + 0.888888889 = -0.489963738 y = -0.489963738 Simplifying y = -0.489963738Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.267741516, -0.489963738}
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