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Simplifying 9y2 + 70y + -833 = 0 Reorder the terms: -833 + 70y + 9y2 = 0 Solving -833 + 70y + 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'. -92.55555556 + 7.777777778y + y2 = 0 Move the constant term to the right: Add '92.55555556' to each side of the equation. -92.55555556 + 7.777777778y + 92.55555556 + y2 = 0 + 92.55555556 Reorder the terms: -92.55555556 + 92.55555556 + 7.777777778y + y2 = 0 + 92.55555556 Combine like terms: -92.55555556 + 92.55555556 = 0.00000000 0.00000000 + 7.777777778y + y2 = 0 + 92.55555556 7.777777778y + y2 = 0 + 92.55555556 Combine like terms: 0 + 92.55555556 = 92.55555556 7.777777778y + y2 = 92.55555556 The y term is 7.777777778y. Take half its coefficient (3.888888889). Square it (15.12345679) and add it to both sides. Add '15.12345679' to each side of the equation. 7.777777778y + 15.12345679 + y2 = 92.55555556 + 15.12345679 Reorder the terms: 15.12345679 + 7.777777778y + y2 = 92.55555556 + 15.12345679 Combine like terms: 92.55555556 + 15.12345679 = 107.67901235 15.12345679 + 7.777777778y + y2 = 107.67901235 Factor a perfect square on the left side: (y + 3.888888889)(y + 3.888888889) = 107.67901235 Calculate the square root of the right side: 10.376849828 Break this problem into two subproblems by setting (y + 3.888888889) equal to 10.376849828 and -10.376849828.Subproblem 1
y + 3.888888889 = 10.376849828 Simplifying y + 3.888888889 = 10.376849828 Reorder the terms: 3.888888889 + y = 10.376849828 Solving 3.888888889 + y = 10.376849828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.888888889' to each side of the equation. 3.888888889 + -3.888888889 + y = 10.376849828 + -3.888888889 Combine like terms: 3.888888889 + -3.888888889 = 0.000000000 0.000000000 + y = 10.376849828 + -3.888888889 y = 10.376849828 + -3.888888889 Combine like terms: 10.376849828 + -3.888888889 = 6.487960939 y = 6.487960939 Simplifying y = 6.487960939Subproblem 2
y + 3.888888889 = -10.376849828 Simplifying y + 3.888888889 = -10.376849828 Reorder the terms: 3.888888889 + y = -10.376849828 Solving 3.888888889 + y = -10.376849828 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.888888889' to each side of the equation. 3.888888889 + -3.888888889 + y = -10.376849828 + -3.888888889 Combine like terms: 3.888888889 + -3.888888889 = 0.000000000 0.000000000 + y = -10.376849828 + -3.888888889 y = -10.376849828 + -3.888888889 Combine like terms: -10.376849828 + -3.888888889 = -14.265738717 y = -14.265738717 Simplifying y = -14.265738717Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.487960939, -14.265738717}
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