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Simplifying y2 + 10y = 5975 Reorder the terms: 10y + y2 = 5975 Solving 10y + y2 = 5975 Solving for variable 'y'. Reorder the terms: -5975 + 10y + y2 = 5975 + -5975 Combine like terms: 5975 + -5975 = 0 -5975 + 10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '5975' to each side of the equation. -5975 + 10y + 5975 + y2 = 0 + 5975 Reorder the terms: -5975 + 5975 + 10y + y2 = 0 + 5975 Combine like terms: -5975 + 5975 = 0 0 + 10y + y2 = 0 + 5975 10y + y2 = 0 + 5975 Combine like terms: 0 + 5975 = 5975 10y + y2 = 5975 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 5975 + 25 Reorder the terms: 25 + 10y + y2 = 5975 + 25 Combine like terms: 5975 + 25 = 6000 25 + 10y + y2 = 6000 Factor a perfect square on the left side: (y + 5)(y + 5) = 6000 Calculate the square root of the right side: 77.459666924 Break this problem into two subproblems by setting (y + 5) equal to 77.459666924 and -77.459666924.Subproblem 1
y + 5 = 77.459666924 Simplifying y + 5 = 77.459666924 Reorder the terms: 5 + y = 77.459666924 Solving 5 + y = 77.459666924 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 77.459666924 + -5 Combine like terms: 5 + -5 = 0 0 + y = 77.459666924 + -5 y = 77.459666924 + -5 Combine like terms: 77.459666924 + -5 = 72.459666924 y = 72.459666924 Simplifying y = 72.459666924Subproblem 2
y + 5 = -77.459666924 Simplifying y + 5 = -77.459666924 Reorder the terms: 5 + y = -77.459666924 Solving 5 + y = -77.459666924 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -77.459666924 + -5 Combine like terms: 5 + -5 = 0 0 + y = -77.459666924 + -5 y = -77.459666924 + -5 Combine like terms: -77.459666924 + -5 = -82.459666924 y = -82.459666924 Simplifying y = -82.459666924Solution
The solution to the problem is based on the solutions from the subproblems. y = {72.459666924, -82.459666924}
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