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Simplifying y2 + -6y + -39 = 0 Reorder the terms: -39 + -6y + y2 = 0 Solving -39 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '39' to each side of the equation. -39 + -6y + 39 + y2 = 0 + 39 Reorder the terms: -39 + 39 + -6y + y2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -6y + y2 = 0 + 39 -6y + y2 = 0 + 39 Combine like terms: 0 + 39 = 39 -6y + y2 = 39 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 39 + 9 Reorder the terms: 9 + -6y + y2 = 39 + 9 Combine like terms: 39 + 9 = 48 9 + -6y + y2 = 48 Factor a perfect square on the left side: (y + -3)(y + -3) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (y + -3) equal to 6.92820323 and -6.92820323.Subproblem 1
y + -3 = 6.92820323 Simplifying y + -3 = 6.92820323 Reorder the terms: -3 + y = 6.92820323 Solving -3 + y = 6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + y = 6.92820323 + 3 y = 6.92820323 + 3 Combine like terms: 6.92820323 + 3 = 9.92820323 y = 9.92820323 Simplifying y = 9.92820323Subproblem 2
y + -3 = -6.92820323 Simplifying y + -3 = -6.92820323 Reorder the terms: -3 + y = -6.92820323 Solving -3 + y = -6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -6.92820323 + 3 Combine like terms: -3 + 3 = 0 0 + y = -6.92820323 + 3 y = -6.92820323 + 3 Combine like terms: -6.92820323 + 3 = -3.92820323 y = -3.92820323 Simplifying y = -3.92820323Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.92820323, -3.92820323}
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