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Simplifying 2y2 + 9y = -8 Reorder the terms: 9y + 2y2 = -8 Solving 9y + 2y2 = -8 Solving for variable 'y'. Reorder the terms: 8 + 9y + 2y2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 9y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4 + 4.5y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.5y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + 4.5y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.5y + y2 = 0 + -4 4.5y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.5y + y2 = -4 The y term is 4.5y. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5y + 5.0625 + y2 = -4 + 5.0625 Reorder the terms: 5.0625 + 4.5y + y2 = -4 + 5.0625 Combine like terms: -4 + 5.0625 = 1.0625 5.0625 + 4.5y + y2 = 1.0625 Factor a perfect square on the left side: (y + 2.25)(y + 2.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (y + 2.25) equal to 1.030776406 and -1.030776406.Subproblem 1
y + 2.25 = 1.030776406 Simplifying y + 2.25 = 1.030776406 Reorder the terms: 2.25 + y = 1.030776406 Solving 2.25 + y = 1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = 1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = 1.030776406 + -2.25 y = 1.030776406 + -2.25 Combine like terms: 1.030776406 + -2.25 = -1.219223594 y = -1.219223594 Simplifying y = -1.219223594Subproblem 2
y + 2.25 = -1.030776406 Simplifying y + 2.25 = -1.030776406 Reorder the terms: 2.25 + y = -1.030776406 Solving 2.25 + y = -1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + y = -1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = -1.030776406 + -2.25 y = -1.030776406 + -2.25 Combine like terms: -1.030776406 + -2.25 = -3.280776406 y = -3.280776406 Simplifying y = -3.280776406Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.219223594, -3.280776406}
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