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Simplifying 50y + -1y2 = 51 Solving 50y + -1y2 = 51 Solving for variable 'y'. Reorder the terms: -51 + 50y + -1y2 = 51 + -51 Combine like terms: 51 + -51 = 0 -51 + 50y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 51 + -50y + y2 = 0 Move the constant term to the right: Add '-51' to each side of the equation. 51 + -50y + -51 + y2 = 0 + -51 Reorder the terms: 51 + -51 + -50y + y2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -50y + y2 = 0 + -51 -50y + y2 = 0 + -51 Combine like terms: 0 + -51 = -51 -50y + y2 = -51 The y term is -50y. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50y + 625 + y2 = -51 + 625 Reorder the terms: 625 + -50y + y2 = -51 + 625 Combine like terms: -51 + 625 = 574 625 + -50y + y2 = 574 Factor a perfect square on the left side: (y + -25)(y + -25) = 574 Calculate the square root of the right side: 23.958297101 Break this problem into two subproblems by setting (y + -25) equal to 23.958297101 and -23.958297101.Subproblem 1
y + -25 = 23.958297101 Simplifying y + -25 = 23.958297101 Reorder the terms: -25 + y = 23.958297101 Solving -25 + y = 23.958297101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + y = 23.958297101 + 25 Combine like terms: -25 + 25 = 0 0 + y = 23.958297101 + 25 y = 23.958297101 + 25 Combine like terms: 23.958297101 + 25 = 48.958297101 y = 48.958297101 Simplifying y = 48.958297101Subproblem 2
y + -25 = -23.958297101 Simplifying y + -25 = -23.958297101 Reorder the terms: -25 + y = -23.958297101 Solving -25 + y = -23.958297101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + y = -23.958297101 + 25 Combine like terms: -25 + 25 = 0 0 + y = -23.958297101 + 25 y = -23.958297101 + 25 Combine like terms: -23.958297101 + 25 = 1.041702899 y = 1.041702899 Simplifying y = 1.041702899Solution
The solution to the problem is based on the solutions from the subproblems. y = {48.958297101, 1.041702899}
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