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Simplifying 0 = y2 + -1y + -400 Reorder the terms: 0 = -400 + -1y + y2 Solving 0 = -400 + -1y + y2 Solving for variable 'y'. Combine like terms: 0 + 400 = 400 400 + y + -1y2 = -400 + -1y + y2 + 400 + y + -1y2 Reorder the terms: 400 + y + -1y2 = -400 + 400 + -1y + y + y2 + -1y2 Combine like terms: -400 + 400 = 0 400 + y + -1y2 = 0 + -1y + y + y2 + -1y2 400 + y + -1y2 = -1y + y + y2 + -1y2 Combine like terms: -1y + y = 0 400 + y + -1y2 = 0 + y2 + -1y2 400 + y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 400 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + -1y + y2 = 0 Move the constant term to the right: Add '400' to each side of the equation. -400 + -1y + 400 + y2 = 0 + 400 Reorder the terms: -400 + 400 + -1y + y2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + -1y + y2 = 0 + 400 -1y + y2 = 0 + 400 Combine like terms: 0 + 400 = 400 -1y + y2 = 400 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 400 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 400 + 0.25 Combine like terms: 400 + 0.25 = 400.25 0.25 + -1y + y2 = 400.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 400.25 Calculate the square root of the right side: 20.006249024 Break this problem into two subproblems by setting (y + 0.5) equal to 20.006249024 and -20.006249024.Subproblem 1
y + 0.5 = 20.006249024 Simplifying y + 0.5 = 20.006249024 Reorder the terms: 0.5 + y = 20.006249024 Solving 0.5 + y = 20.006249024 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 20.006249024 + -0.5 y = 20.006249024 + -0.5 Combine like terms: 20.006249024 + -0.5 = 19.506249024 y = 19.506249024 Simplifying y = 19.506249024Subproblem 2
y + 0.5 = -20.006249024 Simplifying y + 0.5 = -20.006249024 Reorder the terms: 0.5 + y = -20.006249024 Solving 0.5 + y = -20.006249024 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -20.006249024 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -20.006249024 + -0.5 y = -20.006249024 + -0.5 Combine like terms: -20.006249024 + -0.5 = -20.506249024 y = -20.506249024 Simplifying y = -20.506249024Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.506249024, -20.506249024}
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