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Simplifying y2 + -12y + y2 + 11 = 0 Reorder the terms: 11 + -12y + y2 + y2 = 0 Combine like terms: y2 + y2 = 2y2 11 + -12y + 2y2 = 0 Solving 11 + -12y + 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'. 5.5 + -6y + y2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -6y + -5.5 + y2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -6y + y2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -6y + y2 = 0 + -5.5 -6y + y2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -6y + y2 = -5.5 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 = -5.5 + 9 Reorder the terms: 9 + -6y + y2 = -5.5 + 9 Combine like terms: -5.5 + 9 = 3.5 9 + -6y + y2 = 3.5 Factor a perfect square on the left side: (y + -3)(y + -3) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (y + -3) equal to 1.870828693 and -1.870828693.Subproblem 1
y + -3 = 1.870828693 Simplifying y + -3 = 1.870828693 Reorder the terms: -3 + y = 1.870828693 Solving -3 + y = 1.870828693 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 = 1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + y = 1.870828693 + 3 y = 1.870828693 + 3 Combine like terms: 1.870828693 + 3 = 4.870828693 y = 4.870828693 Simplifying y = 4.870828693Subproblem 2
y + -3 = -1.870828693 Simplifying y + -3 = -1.870828693 Reorder the terms: -3 + y = -1.870828693 Solving -3 + y = -1.870828693 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 = -1.870828693 + 3 Combine like terms: -3 + 3 = 0 0 + y = -1.870828693 + 3 y = -1.870828693 + 3 Combine like terms: -1.870828693 + 3 = 1.129171307 y = 1.129171307 Simplifying y = 1.129171307Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.870828693, 1.129171307}
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