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Simplifying 2y2 + 11y + -18 = 0 Reorder the terms: -18 + 11y + 2y2 = 0 Solving -18 + 11y + 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'. -9 + 5.5y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 5.5y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + 5.5y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 5.5y + y2 = 0 + 9 5.5y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 5.5y + y2 = 9 The y term is 5.5y. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5y + 7.5625 + y2 = 9 + 7.5625 Reorder the terms: 7.5625 + 5.5y + y2 = 9 + 7.5625 Combine like terms: 9 + 7.5625 = 16.5625 7.5625 + 5.5y + y2 = 16.5625 Factor a perfect square on the left side: (y + 2.75)(y + 2.75) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (y + 2.75) equal to 4.069705149 and -4.069705149.Subproblem 1
y + 2.75 = 4.069705149 Simplifying y + 2.75 = 4.069705149 Reorder the terms: 2.75 + y = 4.069705149 Solving 2.75 + y = 4.069705149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 4.069705149 + -2.75 y = 4.069705149 + -2.75 Combine like terms: 4.069705149 + -2.75 = 1.319705149 y = 1.319705149 Simplifying y = 1.319705149Subproblem 2
y + 2.75 = -4.069705149 Simplifying y + 2.75 = -4.069705149 Reorder the terms: 2.75 + y = -4.069705149 Solving 2.75 + y = -4.069705149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -4.069705149 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -4.069705149 + -2.75 y = -4.069705149 + -2.75 Combine like terms: -4.069705149 + -2.75 = -6.819705149 y = -6.819705149 Simplifying y = -6.819705149Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.319705149, -6.819705149}
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