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Simplifying y2 + -40y + 140 = 0 Reorder the terms: 140 + -40y + y2 = 0 Solving 140 + -40y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-140' to each side of the equation. 140 + -40y + -140 + y2 = 0 + -140 Reorder the terms: 140 + -140 + -40y + y2 = 0 + -140 Combine like terms: 140 + -140 = 0 0 + -40y + y2 = 0 + -140 -40y + y2 = 0 + -140 Combine like terms: 0 + -140 = -140 -40y + y2 = -140 The y term is -40y. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40y + 400 + y2 = -140 + 400 Reorder the terms: 400 + -40y + y2 = -140 + 400 Combine like terms: -140 + 400 = 260 400 + -40y + y2 = 260 Factor a perfect square on the left side: (y + -20)(y + -20) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (y + -20) equal to 16.124515497 and -16.124515497.Subproblem 1
y + -20 = 16.124515497 Simplifying y + -20 = 16.124515497 Reorder the terms: -20 + y = 16.124515497 Solving -20 + y = 16.124515497 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = 16.124515497 + 20 Combine like terms: -20 + 20 = 0 0 + y = 16.124515497 + 20 y = 16.124515497 + 20 Combine like terms: 16.124515497 + 20 = 36.124515497 y = 36.124515497 Simplifying y = 36.124515497Subproblem 2
y + -20 = -16.124515497 Simplifying y + -20 = -16.124515497 Reorder the terms: -20 + y = -16.124515497 Solving -20 + y = -16.124515497 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = -16.124515497 + 20 Combine like terms: -20 + 20 = 0 0 + y = -16.124515497 + 20 y = -16.124515497 + 20 Combine like terms: -16.124515497 + 20 = 3.875484503 y = 3.875484503 Simplifying y = 3.875484503Solution
The solution to the problem is based on the solutions from the subproblems. y = {36.124515497, 3.875484503}
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