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Simplifying (2y2) + 7y + -78 = 0 Reorder the terms: -78 + 7y + (2y2) = 0 Solving -78 + 7y + (2y2) = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -39 + 3.5y + y2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + 3.5y + 39 + y2 = 0 + 39 Reorder the terms: -39 + 39 + 3.5y + y2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + 3.5y + y2 = 0 + 39 3.5y + y2 = 0 + 39 Combine like terms: 0 + 39 = 39 3.5y + y2 = 39 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 39 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 39 + 3.0625 Combine like terms: 39 + 3.0625 = 42.0625 3.0625 + 3.5y + y2 = 42.0625 Factor a perfect square on the left side: ((y) + 1.75)((y) + 1.75) = 42.0625 Calculate the square root of the right side: 6.485560886 Break this problem into two subproblems by setting ((y) + 1.75) equal to 6.485560886 and -6.485560886.Subproblem 1
(y) + 1.75 = 6.485560886 Simplifying (y) + 1.75 = 6.485560886 y + 1.75 = 6.485560886 Reorder the terms: 1.75 + y = 6.485560886 Solving 1.75 + y = 6.485560886 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 6.485560886 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 6.485560886 + -1.75 y = 6.485560886 + -1.75 Combine like terms: 6.485560886 + -1.75 = 4.735560886 y = 4.735560886 Simplifying y = 4.735560886Subproblem 2
(y) + 1.75 = -6.485560886 Simplifying (y) + 1.75 = -6.485560886 y + 1.75 = -6.485560886 Reorder the terms: 1.75 + y = -6.485560886 Solving 1.75 + y = -6.485560886 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -6.485560886 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -6.485560886 + -1.75 y = -6.485560886 + -1.75 Combine like terms: -6.485560886 + -1.75 = -8.235560886 y = -8.235560886 Simplifying y = -8.235560886Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.735560886, -8.235560886}
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