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Simplifying 13y2 + 216y + -36 = 0 Reorder the terms: -36 + 216y + 13y2 = 0 Solving -36 + 216y + 13y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -2.769230769 + 16.61538462y + y2 = 0 Move the constant term to the right: Add '2.769230769' to each side of the equation. -2.769230769 + 16.61538462y + 2.769230769 + y2 = 0 + 2.769230769 Reorder the terms: -2.769230769 + 2.769230769 + 16.61538462y + y2 = 0 + 2.769230769 Combine like terms: -2.769230769 + 2.769230769 = 0.000000000 0.000000000 + 16.61538462y + y2 = 0 + 2.769230769 16.61538462y + y2 = 0 + 2.769230769 Combine like terms: 0 + 2.769230769 = 2.769230769 16.61538462y + y2 = 2.769230769 The y term is 16.61538462y. Take half its coefficient (8.30769231). Square it (69.01775152) and add it to both sides. Add '69.01775152' to each side of the equation. 16.61538462y + 69.01775152 + y2 = 2.769230769 + 69.01775152 Reorder the terms: 69.01775152 + 16.61538462y + y2 = 2.769230769 + 69.01775152 Combine like terms: 2.769230769 + 69.01775152 = 71.786982289 69.01775152 + 16.61538462y + y2 = 71.786982289 Factor a perfect square on the left side: (y + 8.30769231)(y + 8.30769231) = 71.786982289 Calculate the square root of the right side: 8.472719887 Break this problem into two subproblems by setting (y + 8.30769231) equal to 8.472719887 and -8.472719887.Subproblem 1
y + 8.30769231 = 8.472719887 Simplifying y + 8.30769231 = 8.472719887 Reorder the terms: 8.30769231 + y = 8.472719887 Solving 8.30769231 + y = 8.472719887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.30769231' to each side of the equation. 8.30769231 + -8.30769231 + y = 8.472719887 + -8.30769231 Combine like terms: 8.30769231 + -8.30769231 = 0.00000000 0.00000000 + y = 8.472719887 + -8.30769231 y = 8.472719887 + -8.30769231 Combine like terms: 8.472719887 + -8.30769231 = 0.165027577 y = 0.165027577 Simplifying y = 0.165027577Subproblem 2
y + 8.30769231 = -8.472719887 Simplifying y + 8.30769231 = -8.472719887 Reorder the terms: 8.30769231 + y = -8.472719887 Solving 8.30769231 + y = -8.472719887 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.30769231' to each side of the equation. 8.30769231 + -8.30769231 + y = -8.472719887 + -8.30769231 Combine like terms: 8.30769231 + -8.30769231 = 0.00000000 0.00000000 + y = -8.472719887 + -8.30769231 y = -8.472719887 + -8.30769231 Combine like terms: -8.472719887 + -8.30769231 = -16.780412197 y = -16.780412197 Simplifying y = -16.780412197Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.165027577, -16.780412197}
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