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Simplifying 3y2 + y + -400 = 0 Reorder the terms: -400 + y + 3y2 = 0 Solving -400 + y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -133.3333333 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + 0.3333333333y + 133.3333333 + y2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + 0.3333333333y + y2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + 0.3333333333y + y2 = 0 + 133.3333333 0.3333333333y + y2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 0.3333333333y + y2 = 133.3333333 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. 0.3333333333y + 0.25 + y2 = 133.3333333 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = 133.3333333 + 0.25 Combine like terms: 133.3333333 + 0.25 = 133.5833333 0.25 + 0.3333333333y + y2 = 133.5833333 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 133.5833333 Calculate the square root of the right side: 11.55782563 Break this problem into two subproblems by setting (y + 0.5) equal to 11.55782563 and -11.55782563.Subproblem 1
y + 0.5 = 11.55782563 Simplifying y + 0.5 = 11.55782563 Reorder the terms: 0.5 + y = 11.55782563 Solving 0.5 + y = 11.55782563 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 = 11.55782563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 11.55782563 + -0.5 y = 11.55782563 + -0.5 Combine like terms: 11.55782563 + -0.5 = 11.05782563 y = 11.05782563 Simplifying y = 11.05782563Subproblem 2
y + 0.5 = -11.55782563 Simplifying y + 0.5 = -11.55782563 Reorder the terms: 0.5 + y = -11.55782563 Solving 0.5 + y = -11.55782563 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 = -11.55782563 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -11.55782563 + -0.5 y = -11.55782563 + -0.5 Combine like terms: -11.55782563 + -0.5 = -12.05782563 y = -12.05782563 Simplifying y = -12.05782563Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.05782563, -12.05782563}
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