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Simplifying y2 + -25y = 100 Reorder the terms: -25y + y2 = 100 Solving -25y + y2 = 100 Solving for variable 'y'. Reorder the terms: -100 + -25y + y2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -25y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -25y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + -25y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -25y + y2 = 0 + 100 -25y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 -25y + y2 = 100 The y term is -25y. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25y + 156.25 + y2 = 100 + 156.25 Reorder the terms: 156.25 + -25y + y2 = 100 + 156.25 Combine like terms: 100 + 156.25 = 256.25 156.25 + -25y + y2 = 256.25 Factor a perfect square on the left side: (y + -12.5)(y + -12.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (y + -12.5) equal to 16.007810594 and -16.007810594.Subproblem 1
y + -12.5 = 16.007810594 Simplifying y + -12.5 = 16.007810594 Reorder the terms: -12.5 + y = 16.007810594 Solving -12.5 + y = 16.007810594 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = 16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = 16.007810594 + 12.5 y = 16.007810594 + 12.5 Combine like terms: 16.007810594 + 12.5 = 28.507810594 y = 28.507810594 Simplifying y = 28.507810594Subproblem 2
y + -12.5 = -16.007810594 Simplifying y + -12.5 = -16.007810594 Reorder the terms: -12.5 + y = -16.007810594 Solving -12.5 + y = -16.007810594 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = -16.007810594 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = -16.007810594 + 12.5 y = -16.007810594 + 12.5 Combine like terms: -16.007810594 + 12.5 = -3.507810594 y = -3.507810594 Simplifying y = -3.507810594Solution
The solution to the problem is based on the solutions from the subproblems. y = {28.507810594, -3.507810594}
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