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Simplifying y2 + 6y = 110 Reorder the terms: 6y + y2 = 110 Solving 6y + y2 = 110 Solving for variable 'y'. Reorder the terms: -110 + 6y + y2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 6y + 110 + y2 = 0 + 110 Reorder the terms: -110 + 110 + 6y + y2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 6y + y2 = 0 + 110 6y + y2 = 0 + 110 Combine like terms: 0 + 110 = 110 6y + y2 = 110 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 = 110 + 9 Reorder the terms: 9 + 6y + y2 = 110 + 9 Combine like terms: 110 + 9 = 119 9 + 6y + y2 = 119 Factor a perfect square on the left side: (y + 3)(y + 3) = 119 Calculate the square root of the right side: 10.908712115 Break this problem into two subproblems by setting (y + 3) equal to 10.908712115 and -10.908712115.Subproblem 1
y + 3 = 10.908712115 Simplifying y + 3 = 10.908712115 Reorder the terms: 3 + y = 10.908712115 Solving 3 + y = 10.908712115 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 = 10.908712115 + -3 Combine like terms: 3 + -3 = 0 0 + y = 10.908712115 + -3 y = 10.908712115 + -3 Combine like terms: 10.908712115 + -3 = 7.908712115 y = 7.908712115 Simplifying y = 7.908712115Subproblem 2
y + 3 = -10.908712115 Simplifying y + 3 = -10.908712115 Reorder the terms: 3 + y = -10.908712115 Solving 3 + y = -10.908712115 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 = -10.908712115 + -3 Combine like terms: 3 + -3 = 0 0 + y = -10.908712115 + -3 y = -10.908712115 + -3 Combine like terms: -10.908712115 + -3 = -13.908712115 y = -13.908712115 Simplifying y = -13.908712115Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.908712115, -13.908712115}
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