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Simplifying 2y2 + -6 = -9y Reorder the terms: -6 + 2y2 = -9y Solving -6 + 2y2 = -9y Solving for variable 'y'. Reorder the terms: -6 + 9y + 2y2 = -9y + 9y Combine like terms: -9y + 9y = 0 -6 + 9y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 4.5y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4.5y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 4.5y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4.5y + y2 = 0 + 3 4.5y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 4.5y + y2 = 3 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 = 3 + 5.0625 Reorder the terms: 5.0625 + 4.5y + y2 = 3 + 5.0625 Combine like terms: 3 + 5.0625 = 8.0625 5.0625 + 4.5y + y2 = 8.0625 Factor a perfect square on the left side: (y + 2.25)(y + 2.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (y + 2.25) equal to 2.839454173 and -2.839454173.Subproblem 1
y + 2.25 = 2.839454173 Simplifying y + 2.25 = 2.839454173 Reorder the terms: 2.25 + y = 2.839454173 Solving 2.25 + y = 2.839454173 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 = 2.839454173 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = 2.839454173 + -2.25 y = 2.839454173 + -2.25 Combine like terms: 2.839454173 + -2.25 = 0.589454173 y = 0.589454173 Simplifying y = 0.589454173Subproblem 2
y + 2.25 = -2.839454173 Simplifying y + 2.25 = -2.839454173 Reorder the terms: 2.25 + y = -2.839454173 Solving 2.25 + y = -2.839454173 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 = -2.839454173 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + y = -2.839454173 + -2.25 y = -2.839454173 + -2.25 Combine like terms: -2.839454173 + -2.25 = -5.089454173 y = -5.089454173 Simplifying y = -5.089454173Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.589454173, -5.089454173}
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