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Simplifying y2 + -19y + 77 = 0 Reorder the terms: 77 + -19y + y2 = 0 Solving 77 + -19y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + -19y + -77 + y2 = 0 + -77 Reorder the terms: 77 + -77 + -19y + y2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -19y + y2 = 0 + -77 -19y + y2 = 0 + -77 Combine like terms: 0 + -77 = -77 -19y + y2 = -77 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = -77 + 90.25 Reorder the terms: 90.25 + -19y + y2 = -77 + 90.25 Combine like terms: -77 + 90.25 = 13.25 90.25 + -19y + y2 = 13.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (y + -9.5) equal to 3.640054945 and -3.640054945.Subproblem 1
y + -9.5 = 3.640054945 Simplifying y + -9.5 = 3.640054945 Reorder the terms: -9.5 + y = 3.640054945 Solving -9.5 + y = 3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 3.640054945 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 3.640054945 + 9.5 y = 3.640054945 + 9.5 Combine like terms: 3.640054945 + 9.5 = 13.140054945 y = 13.140054945 Simplifying y = 13.140054945Subproblem 2
y + -9.5 = -3.640054945 Simplifying y + -9.5 = -3.640054945 Reorder the terms: -9.5 + y = -3.640054945 Solving -9.5 + y = -3.640054945 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -3.640054945 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -3.640054945 + 9.5 y = -3.640054945 + 9.5 Combine like terms: -3.640054945 + 9.5 = 5.859945055 y = 5.859945055 Simplifying y = 5.859945055Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.140054945, 5.859945055}
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