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Simplifying 581 + 840y + 295y2 = 0 Solving 581 + 840y + 295y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 295 the coefficient of the squared term: Divide each side by '295'. 1.969491525 + 2.847457627y + y2 = 0 Move the constant term to the right: Add '-1.969491525' to each side of the equation. 1.969491525 + 2.847457627y + -1.969491525 + y2 = 0 + -1.969491525 Reorder the terms: 1.969491525 + -1.969491525 + 2.847457627y + y2 = 0 + -1.969491525 Combine like terms: 1.969491525 + -1.969491525 = 0.000000000 0.000000000 + 2.847457627y + y2 = 0 + -1.969491525 2.847457627y + y2 = 0 + -1.969491525 Combine like terms: 0 + -1.969491525 = -1.969491525 2.847457627y + y2 = -1.969491525 The y term is 2.847457627y. Take half its coefficient (1.423728814). Square it (2.027003736) and add it to both sides. Add '2.027003736' to each side of the equation. 2.847457627y + 2.027003736 + y2 = -1.969491525 + 2.027003736 Reorder the terms: 2.027003736 + 2.847457627y + y2 = -1.969491525 + 2.027003736 Combine like terms: -1.969491525 + 2.027003736 = 0.057512211 2.027003736 + 2.847457627y + y2 = 0.057512211 Factor a perfect square on the left side: (y + 1.423728814)(y + 1.423728814) = 0.057512211 Calculate the square root of the right side: 0.239817037 Break this problem into two subproblems by setting (y + 1.423728814) equal to 0.239817037 and -0.239817037.Subproblem 1
y + 1.423728814 = 0.239817037 Simplifying y + 1.423728814 = 0.239817037 Reorder the terms: 1.423728814 + y = 0.239817037 Solving 1.423728814 + y = 0.239817037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.423728814' to each side of the equation. 1.423728814 + -1.423728814 + y = 0.239817037 + -1.423728814 Combine like terms: 1.423728814 + -1.423728814 = 0.000000000 0.000000000 + y = 0.239817037 + -1.423728814 y = 0.239817037 + -1.423728814 Combine like terms: 0.239817037 + -1.423728814 = -1.183911777 y = -1.183911777 Simplifying y = -1.183911777Subproblem 2
y + 1.423728814 = -0.239817037 Simplifying y + 1.423728814 = -0.239817037 Reorder the terms: 1.423728814 + y = -0.239817037 Solving 1.423728814 + y = -0.239817037 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.423728814' to each side of the equation. 1.423728814 + -1.423728814 + y = -0.239817037 + -1.423728814 Combine like terms: 1.423728814 + -1.423728814 = 0.000000000 0.000000000 + y = -0.239817037 + -1.423728814 y = -0.239817037 + -1.423728814 Combine like terms: -0.239817037 + -1.423728814 = -1.663545851 y = -1.663545851 Simplifying y = -1.663545851Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.183911777, -1.663545851}
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