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Simplifying 0 = -1y2 + 100y + 10000 Reorder the terms: 0 = 10000 + 100y + -1y2 Solving 0 = 10000 + 100y + -1y2 Solving for variable 'y'. Combine like terms: 0 + -10000 = -10000 -10000 + -100y + y2 = 10000 + 100y + -1y2 + -10000 + -100y + y2 Reorder the terms: -10000 + -100y + y2 = 10000 + -10000 + 100y + -100y + -1y2 + y2 Combine like terms: 10000 + -10000 = 0 -10000 + -100y + y2 = 0 + 100y + -100y + -1y2 + y2 -10000 + -100y + y2 = 100y + -100y + -1y2 + y2 Combine like terms: 100y + -100y = 0 -10000 + -100y + y2 = 0 + -1y2 + y2 -10000 + -100y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -10000 + -100y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + -100y + 10000 + y2 = 0 + 10000 Reorder the terms: -10000 + 10000 + -100y + y2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + -100y + y2 = 0 + 10000 -100y + y2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 -100y + y2 = 10000 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 = 10000 + 2500 Reorder the terms: 2500 + -100y + y2 = 10000 + 2500 Combine like terms: 10000 + 2500 = 12500 2500 + -100y + y2 = 12500 Factor a perfect square on the left side: (y + -50)(y + -50) = 12500 Calculate the square root of the right side: 111.803398875 Break this problem into two subproblems by setting (y + -50) equal to 111.803398875 and -111.803398875.Subproblem 1
y + -50 = 111.803398875 Simplifying y + -50 = 111.803398875 Reorder the terms: -50 + y = 111.803398875 Solving -50 + y = 111.803398875 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 = 111.803398875 + 50 Combine like terms: -50 + 50 = 0 0 + y = 111.803398875 + 50 y = 111.803398875 + 50 Combine like terms: 111.803398875 + 50 = 161.803398875 y = 161.803398875 Simplifying y = 161.803398875Subproblem 2
y + -50 = -111.803398875 Simplifying y + -50 = -111.803398875 Reorder the terms: -50 + y = -111.803398875 Solving -50 + y = -111.803398875 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 = -111.803398875 + 50 Combine like terms: -50 + 50 = 0 0 + y = -111.803398875 + 50 y = -111.803398875 + 50 Combine like terms: -111.803398875 + 50 = -61.803398875 y = -61.803398875 Simplifying y = -61.803398875Solution
The solution to the problem is based on the solutions from the subproblems. y = {161.803398875, -61.803398875}
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