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Simplifying -6y2 + -11y + 34 = -5 Reorder the terms: 34 + -11y + -6y2 = -5 Solving 34 + -11y + -6y2 = -5 Solving for variable 'y'. Reorder the terms: 34 + 5 + -11y + -6y2 = -5 + 5 Combine like terms: 34 + 5 = 39 39 + -11y + -6y2 = -5 + 5 Combine like terms: -5 + 5 = 0 39 + -11y + -6y2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -6.5 + 1.833333333y + y2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 1.833333333y + 6.5 + y2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 1.833333333y + y2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 1.833333333y + y2 = 0 + 6.5 1.833333333y + y2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 1.833333333y + y2 = 6.5 The y term is 1.833333333y. Take half its coefficient (0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. 1.833333333y + 0.8402777775 + y2 = 6.5 + 0.8402777775 Reorder the terms: 0.8402777775 + 1.833333333y + y2 = 6.5 + 0.8402777775 Combine like terms: 6.5 + 0.8402777775 = 7.3402777775 0.8402777775 + 1.833333333y + y2 = 7.3402777775 Factor a perfect square on the left side: (y + 0.9166666665)(y + 0.9166666665) = 7.3402777775 Calculate the square root of the right side: 2.709294701 Break this problem into two subproblems by setting (y + 0.9166666665) equal to 2.709294701 and -2.709294701.Subproblem 1
y + 0.9166666665 = 2.709294701 Simplifying y + 0.9166666665 = 2.709294701 Reorder the terms: 0.9166666665 + y = 2.709294701 Solving 0.9166666665 + y = 2.709294701 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + y = 2.709294701 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + y = 2.709294701 + -0.9166666665 y = 2.709294701 + -0.9166666665 Combine like terms: 2.709294701 + -0.9166666665 = 1.7926280345 y = 1.7926280345 Simplifying y = 1.7926280345Subproblem 2
y + 0.9166666665 = -2.709294701 Simplifying y + 0.9166666665 = -2.709294701 Reorder the terms: 0.9166666665 + y = -2.709294701 Solving 0.9166666665 + y = -2.709294701 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.9166666665' to each side of the equation. 0.9166666665 + -0.9166666665 + y = -2.709294701 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + y = -2.709294701 + -0.9166666665 y = -2.709294701 + -0.9166666665 Combine like terms: -2.709294701 + -0.9166666665 = -3.6259613675 y = -3.6259613675 Simplifying y = -3.6259613675Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.7926280345, -3.6259613675}
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