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Simplifying 9y2 + -46y + 52 = 0 Reorder the terms: 52 + -46y + 9y2 = 0 Solving 52 + -46y + 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'. 5.777777778 + -5.111111111y + y2 = 0 Move the constant term to the right: Add '-5.777777778' to each side of the equation. 5.777777778 + -5.111111111y + -5.777777778 + y2 = 0 + -5.777777778 Reorder the terms: 5.777777778 + -5.777777778 + -5.111111111y + y2 = 0 + -5.777777778 Combine like terms: 5.777777778 + -5.777777778 = 0.000000000 0.000000000 + -5.111111111y + y2 = 0 + -5.777777778 -5.111111111y + y2 = 0 + -5.777777778 Combine like terms: 0 + -5.777777778 = -5.777777778 -5.111111111y + y2 = -5.777777778 The y term is -5.111111111y. Take half its coefficient (-2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. -5.111111111y + 6.530864200 + y2 = -5.777777778 + 6.530864200 Reorder the terms: 6.530864200 + -5.111111111y + y2 = -5.777777778 + 6.530864200 Combine like terms: -5.777777778 + 6.530864200 = 0.753086422 6.530864200 + -5.111111111y + y2 = 0.753086422 Factor a perfect square on the left side: (y + -2.555555556)(y + -2.555555556) = 0.753086422 Calculate the square root of the right side: 0.867805521 Break this problem into two subproblems by setting (y + -2.555555556) equal to 0.867805521 and -0.867805521.Subproblem 1
y + -2.555555556 = 0.867805521 Simplifying y + -2.555555556 = 0.867805521 Reorder the terms: -2.555555556 + y = 0.867805521 Solving -2.555555556 + y = 0.867805521 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + y = 0.867805521 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + y = 0.867805521 + 2.555555556 y = 0.867805521 + 2.555555556 Combine like terms: 0.867805521 + 2.555555556 = 3.423361077 y = 3.423361077 Simplifying y = 3.423361077Subproblem 2
y + -2.555555556 = -0.867805521 Simplifying y + -2.555555556 = -0.867805521 Reorder the terms: -2.555555556 + y = -0.867805521 Solving -2.555555556 + y = -0.867805521 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + y = -0.867805521 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + y = -0.867805521 + 2.555555556 y = -0.867805521 + 2.555555556 Combine like terms: -0.867805521 + 2.555555556 = 1.687750035 y = 1.687750035 Simplifying y = 1.687750035Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.423361077, 1.687750035}
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