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Simplifying 26y2 + 24y + -5 = 0 Reorder the terms: -5 + 24y + 26y2 = 0 Solving -5 + 24y + 26y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. -0.1923076923 + 0.9230769231y + y2 = 0 Move the constant term to the right: Add '0.1923076923' to each side of the equation. -0.1923076923 + 0.9230769231y + 0.1923076923 + y2 = 0 + 0.1923076923 Reorder the terms: -0.1923076923 + 0.1923076923 + 0.9230769231y + y2 = 0 + 0.1923076923 Combine like terms: -0.1923076923 + 0.1923076923 = 0.0000000000 0.0000000000 + 0.9230769231y + y2 = 0 + 0.1923076923 0.9230769231y + y2 = 0 + 0.1923076923 Combine like terms: 0 + 0.1923076923 = 0.1923076923 0.9230769231y + y2 = 0.1923076923 The y term is 0.9230769231y. Take half its coefficient (0.4615384616). Square it (0.2130177515) and add it to both sides. Add '0.2130177515' to each side of the equation. 0.9230769231y + 0.2130177515 + y2 = 0.1923076923 + 0.2130177515 Reorder the terms: 0.2130177515 + 0.9230769231y + y2 = 0.1923076923 + 0.2130177515 Combine like terms: 0.1923076923 + 0.2130177515 = 0.4053254438 0.2130177515 + 0.9230769231y + y2 = 0.4053254438 Factor a perfect square on the left side: (y + 0.4615384616)(y + 0.4615384616) = 0.4053254438 Calculate the square root of the right side: 0.636651745 Break this problem into two subproblems by setting (y + 0.4615384616) equal to 0.636651745 and -0.636651745.Subproblem 1
y + 0.4615384616 = 0.636651745 Simplifying y + 0.4615384616 = 0.636651745 Reorder the terms: 0.4615384616 + y = 0.636651745 Solving 0.4615384616 + y = 0.636651745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + y = 0.636651745 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + y = 0.636651745 + -0.4615384616 y = 0.636651745 + -0.4615384616 Combine like terms: 0.636651745 + -0.4615384616 = 0.1751132834 y = 0.1751132834 Simplifying y = 0.1751132834Subproblem 2
y + 0.4615384616 = -0.636651745 Simplifying y + 0.4615384616 = -0.636651745 Reorder the terms: 0.4615384616 + y = -0.636651745 Solving 0.4615384616 + y = -0.636651745 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4615384616' to each side of the equation. 0.4615384616 + -0.4615384616 + y = -0.636651745 + -0.4615384616 Combine like terms: 0.4615384616 + -0.4615384616 = 0.0000000000 0.0000000000 + y = -0.636651745 + -0.4615384616 y = -0.636651745 + -0.4615384616 Combine like terms: -0.636651745 + -0.4615384616 = -1.0981902066 y = -1.0981902066 Simplifying y = -1.0981902066Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.1751132834, -1.0981902066}
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