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Simplifying y2 + 72.25 = -17y Reorder the terms: 72.25 + y2 = -17y Solving 72.25 + y2 = -17y Solving for variable 'y'. Reorder the terms: 72.25 + 17y + y2 = -17y + 17y Combine like terms: -17y + 17y = 0 72.25 + 17y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-72.25' to each side of the equation. 72.25 + 17y + -72.25 + y2 = 0 + -72.25 Reorder the terms: 72.25 + -72.25 + 17y + y2 = 0 + -72.25 Combine like terms: 72.25 + -72.25 = 0.00 0.00 + 17y + y2 = 0 + -72.25 17y + y2 = 0 + -72.25 Combine like terms: 0 + -72.25 = -72.25 17y + y2 = -72.25 The y term is 17y. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17y + 72.25 + y2 = -72.25 + 72.25 Reorder the terms: 72.25 + 17y + y2 = -72.25 + 72.25 Combine like terms: -72.25 + 72.25 = 0.00 72.25 + 17y + y2 = 0.00 Factor a perfect square on the left side: (y + 8.5)(y + 8.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (y + 8.5) equal to 0.00 and 0.00.Subproblem 1
y + 8.5 = 0.00 Simplifying y + 8.5 = 0.00 Reorder the terms: 8.5 + y = 0.00 Solving 8.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = 0.00 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 0.00 + -8.5 y = 0.00 + -8.5 Combine like terms: 0.00 + -8.5 = -8.5 y = -8.5 Simplifying y = -8.5Subproblem 2
y + 8.5 = 0.00 Simplifying y + 8.5 = 0.00 Reorder the terms: 8.5 + y = 0.00 Solving 8.5 + y = 0.00 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = 0.00 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 0.00 + -8.5 y = 0.00 + -8.5 Combine like terms: 0.00 + -8.5 = -8.5 y = -8.5 Simplifying y = -8.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {-8.5, -8.5}
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