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Simplifying 4y2 + 35y + -71 = 0 Reorder the terms: -71 + 35y + 4y2 = 0 Solving -71 + 35y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.75 + 8.75y + y2 = 0 Move the constant term to the right: Add '17.75' to each side of the equation. -17.75 + 8.75y + 17.75 + y2 = 0 + 17.75 Reorder the terms: -17.75 + 17.75 + 8.75y + y2 = 0 + 17.75 Combine like terms: -17.75 + 17.75 = 0.00 0.00 + 8.75y + y2 = 0 + 17.75 8.75y + y2 = 0 + 17.75 Combine like terms: 0 + 17.75 = 17.75 8.75y + y2 = 17.75 The y term is 8.75y. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75y + 19.140625 + y2 = 17.75 + 19.140625 Reorder the terms: 19.140625 + 8.75y + y2 = 17.75 + 19.140625 Combine like terms: 17.75 + 19.140625 = 36.890625 19.140625 + 8.75y + y2 = 36.890625 Factor a perfect square on the left side: (y + 4.375)(y + 4.375) = 36.890625 Calculate the square root of the right side: 6.073765307 Break this problem into two subproblems by setting (y + 4.375) equal to 6.073765307 and -6.073765307.Subproblem 1
y + 4.375 = 6.073765307 Simplifying y + 4.375 = 6.073765307 Reorder the terms: 4.375 + y = 6.073765307 Solving 4.375 + y = 6.073765307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + y = 6.073765307 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + y = 6.073765307 + -4.375 y = 6.073765307 + -4.375 Combine like terms: 6.073765307 + -4.375 = 1.698765307 y = 1.698765307 Simplifying y = 1.698765307Subproblem 2
y + 4.375 = -6.073765307 Simplifying y + 4.375 = -6.073765307 Reorder the terms: 4.375 + y = -6.073765307 Solving 4.375 + y = -6.073765307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + y = -6.073765307 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + y = -6.073765307 + -4.375 y = -6.073765307 + -4.375 Combine like terms: -6.073765307 + -4.375 = -10.448765307 y = -10.448765307 Simplifying y = -10.448765307Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.698765307, -10.448765307}
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