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Simplifying 100 + -100y = -1y2 Solving 100 + -100y = -1y2 Solving for variable 'y'. Combine like terms: -1y2 + y2 = 0 100 + -100y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -100y + -100 + y2 = 0 + -100 Reorder the terms: 100 + -100 + -100y + y2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -100y + y2 = 0 + -100 -100y + y2 = 0 + -100 Combine like terms: 0 + -100 = -100 -100y + y2 = -100 The y term is -100y. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100y + 2500 + y2 = -100 + 2500 Reorder the terms: 2500 + -100y + y2 = -100 + 2500 Combine like terms: -100 + 2500 = 2400 2500 + -100y + y2 = 2400 Factor a perfect square on the left side: (y + -50)(y + -50) = 2400 Calculate the square root of the right side: 48.989794856 Break this problem into two subproblems by setting (y + -50) equal to 48.989794856 and -48.989794856.Subproblem 1
y + -50 = 48.989794856 Simplifying y + -50 = 48.989794856 Reorder the terms: -50 + y = 48.989794856 Solving -50 + y = 48.989794856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y = 48.989794856 + 50 Combine like terms: -50 + 50 = 0 0 + y = 48.989794856 + 50 y = 48.989794856 + 50 Combine like terms: 48.989794856 + 50 = 98.989794856 y = 98.989794856 Simplifying y = 98.989794856Subproblem 2
y + -50 = -48.989794856 Simplifying y + -50 = -48.989794856 Reorder the terms: -50 + y = -48.989794856 Solving -50 + y = -48.989794856 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + y = -48.989794856 + 50 Combine like terms: -50 + 50 = 0 0 + y = -48.989794856 + 50 y = -48.989794856 + 50 Combine like terms: -48.989794856 + 50 = 1.010205144 y = 1.010205144 Simplifying y = 1.010205144Solution
The solution to the problem is based on the solutions from the subproblems. y = {98.989794856, 1.010205144}
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