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Simplifying (4y2) + -19y + -60 = 0 Reorder the terms: -60 + -19y + (4y2) = 0 Solving -60 + -19y + (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'. -15 + -4.75y + y2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -4.75y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + -4.75y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4.75y + y2 = 0 + 15 -4.75y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4.75y + y2 = 15 The y term is -4.75y. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75y + 5.640625 + y2 = 15 + 5.640625 Reorder the terms: 5.640625 + -4.75y + y2 = 15 + 5.640625 Combine like terms: 15 + 5.640625 = 20.640625 5.640625 + -4.75y + y2 = 20.640625 Factor a perfect square on the left side: ((y) + -2.375)((y) + -2.375) = 20.640625 Calculate the square root of the right side: 4.543195461 Break this problem into two subproblems by setting ((y) + -2.375) equal to 4.543195461 and -4.543195461.Subproblem 1
(y) + -2.375 = 4.543195461 Simplifying (y) + -2.375 = 4.543195461 y + -2.375 = 4.543195461 Reorder the terms: -2.375 + y = 4.543195461 Solving -2.375 + y = 4.543195461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + y = 4.543195461 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + y = 4.543195461 + 2.375 y = 4.543195461 + 2.375 Combine like terms: 4.543195461 + 2.375 = 6.918195461 y = 6.918195461 Simplifying y = 6.918195461Subproblem 2
(y) + -2.375 = -4.543195461 Simplifying (y) + -2.375 = -4.543195461 y + -2.375 = -4.543195461 Reorder the terms: -2.375 + y = -4.543195461 Solving -2.375 + y = -4.543195461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + y = -4.543195461 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + y = -4.543195461 + 2.375 y = -4.543195461 + 2.375 Combine like terms: -4.543195461 + 2.375 = -2.168195461 y = -2.168195461 Simplifying y = -2.168195461Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.918195461, -2.168195461}
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