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Simplifying y2 + -4y + -124 = 0 Reorder the terms: -124 + -4y + y2 = 0 Solving -124 + -4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + -4y + 124 + y2 = 0 + 124 Reorder the terms: -124 + 124 + -4y + y2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + -4y + y2 = 0 + 124 -4y + y2 = 0 + 124 Combine like terms: 0 + 124 = 124 -4y + y2 = 124 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 124 + 4 Reorder the terms: 4 + -4y + y2 = 124 + 4 Combine like terms: 124 + 4 = 128 4 + -4y + y2 = 128 Factor a perfect square on the left side: (y + -2)(y + -2) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (y + -2) equal to 11.313708499 and -11.313708499.Subproblem 1
y + -2 = 11.313708499 Simplifying y + -2 = 11.313708499 Reorder the terms: -2 + y = 11.313708499 Solving -2 + y = 11.313708499 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 11.313708499 + 2 Combine like terms: -2 + 2 = 0 0 + y = 11.313708499 + 2 y = 11.313708499 + 2 Combine like terms: 11.313708499 + 2 = 13.313708499 y = 13.313708499 Simplifying y = 13.313708499Subproblem 2
y + -2 = -11.313708499 Simplifying y + -2 = -11.313708499 Reorder the terms: -2 + y = -11.313708499 Solving -2 + y = -11.313708499 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -11.313708499 + 2 Combine like terms: -2 + 2 = 0 0 + y = -11.313708499 + 2 y = -11.313708499 + 2 Combine like terms: -11.313708499 + 2 = -9.313708499 y = -9.313708499 Simplifying y = -9.313708499Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.313708499, -9.313708499}
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