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Simplifying y2 + -6y = 11 Reorder the terms: -6y + y2 = 11 Solving -6y + y2 = 11 Solving for variable 'y'. Reorder the terms: -11 + -6y + y2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -6y + 11 + y2 = 0 + 11 Reorder the terms: -11 + 11 + -6y + y2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6y + y2 = 0 + 11 -6y + y2 = 0 + 11 Combine like terms: 0 + 11 = 11 -6y + y2 = 11 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 = 11 + 9 Reorder the terms: 9 + -6y + y2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + -6y + y2 = 20 Factor a perfect square on the left side: (y + -3)(y + -3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (y + -3) equal to 4.472135955 and -4.472135955.Subproblem 1
y + -3 = 4.472135955 Simplifying y + -3 = 4.472135955 Reorder the terms: -3 + y = 4.472135955 Solving -3 + y = 4.472135955 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 = 4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.472135955 + 3 y = 4.472135955 + 3 Combine like terms: 4.472135955 + 3 = 7.472135955 y = 7.472135955 Simplifying y = 7.472135955Subproblem 2
y + -3 = -4.472135955 Simplifying y + -3 = -4.472135955 Reorder the terms: -3 + y = -4.472135955 Solving -3 + y = -4.472135955 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 = -4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.472135955 + 3 y = -4.472135955 + 3 Combine like terms: -4.472135955 + 3 = -1.472135955 y = -1.472135955 Simplifying y = -1.472135955Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.472135955, -1.472135955}
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