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Simplifying (y + -5)(y + -5) = 2y2 + 5y + 11 Reorder the terms: (-5 + y)(y + -5) = 2y2 + 5y + 11 Reorder the terms: (-5 + y)(-5 + y) = 2y2 + 5y + 11 Multiply (-5 + y) * (-5 + y) (-5(-5 + y) + y(-5 + y)) = 2y2 + 5y + 11 ((-5 * -5 + y * -5) + y(-5 + y)) = 2y2 + 5y + 11 ((25 + -5y) + y(-5 + y)) = 2y2 + 5y + 11 (25 + -5y + (-5 * y + y * y)) = 2y2 + 5y + 11 (25 + -5y + (-5y + y2)) = 2y2 + 5y + 11 Combine like terms: -5y + -5y = -10y (25 + -10y + y2) = 2y2 + 5y + 11 Reorder the terms: 25 + -10y + y2 = 11 + 5y + 2y2 Solving 25 + -10y + y2 = 11 + 5y + 2y2 Solving for variable 'y'. Reorder the terms: 25 + -11 + -10y + -5y + y2 + -2y2 = 11 + 5y + 2y2 + -11 + -5y + -2y2 Combine like terms: 25 + -11 = 14 14 + -10y + -5y + y2 + -2y2 = 11 + 5y + 2y2 + -11 + -5y + -2y2 Combine like terms: -10y + -5y = -15y 14 + -15y + y2 + -2y2 = 11 + 5y + 2y2 + -11 + -5y + -2y2 Combine like terms: y2 + -2y2 = -1y2 14 + -15y + -1y2 = 11 + 5y + 2y2 + -11 + -5y + -2y2 Reorder the terms: 14 + -15y + -1y2 = 11 + -11 + 5y + -5y + 2y2 + -2y2 Combine like terms: 11 + -11 = 0 14 + -15y + -1y2 = 0 + 5y + -5y + 2y2 + -2y2 14 + -15y + -1y2 = 5y + -5y + 2y2 + -2y2 Combine like terms: 5y + -5y = 0 14 + -15y + -1y2 = 0 + 2y2 + -2y2 14 + -15y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 14 + -15y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 15y + y2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 15y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 15y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 15y + y2 = 0 + 14 15y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 15y + y2 = 14 The y term is 15y. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15y + 56.25 + y2 = 14 + 56.25 Reorder the terms: 56.25 + 15y + y2 = 14 + 56.25 Combine like terms: 14 + 56.25 = 70.25 56.25 + 15y + y2 = 70.25 Factor a perfect square on the left side: (y + 7.5)(y + 7.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (y + 7.5) equal to 8.381527307 and -8.381527307.Subproblem 1
y + 7.5 = 8.381527307 Simplifying y + 7.5 = 8.381527307 Reorder the terms: 7.5 + y = 8.381527307 Solving 7.5 + y = 8.381527307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = 8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = 8.381527307 + -7.5 y = 8.381527307 + -7.5 Combine like terms: 8.381527307 + -7.5 = 0.881527307 y = 0.881527307 Simplifying y = 0.881527307Subproblem 2
y + 7.5 = -8.381527307 Simplifying y + 7.5 = -8.381527307 Reorder the terms: 7.5 + y = -8.381527307 Solving 7.5 + y = -8.381527307 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + y = -8.381527307 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + y = -8.381527307 + -7.5 y = -8.381527307 + -7.5 Combine like terms: -8.381527307 + -7.5 = -15.881527307 y = -15.881527307 Simplifying y = -15.881527307Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.881527307, -15.881527307}
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