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Simplifying 2y2 + 5y + 10 = 40 Reorder the terms: 10 + 5y + 2y2 = 40 Solving 10 + 5y + 2y2 = 40 Solving for variable 'y'. Reorder the terms: 10 + -40 + 5y + 2y2 = 40 + -40 Combine like terms: 10 + -40 = -30 -30 + 5y + 2y2 = 40 + -40 Combine like terms: 40 + -40 = 0 -30 + 5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + 2.5y + y2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 2.5y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 2.5y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 2.5y + y2 = 0 + 15 2.5y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 2.5y + y2 = 15 The y term is 2.5y. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5y + 1.5625 + y2 = 15 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = 15 + 1.5625 Combine like terms: 15 + 1.5625 = 16.5625 1.5625 + 2.5y + y2 = 16.5625 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (y + 1.25) equal to 4.069705149 and -4.069705149.Subproblem 1
y + 1.25 = 4.069705149 Simplifying y + 1.25 = 4.069705149 Reorder the terms: 1.25 + y = 4.069705149 Solving 1.25 + y = 4.069705149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = 4.069705149 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 4.069705149 + -1.25 y = 4.069705149 + -1.25 Combine like terms: 4.069705149 + -1.25 = 2.819705149 y = 2.819705149 Simplifying y = 2.819705149Subproblem 2
y + 1.25 = -4.069705149 Simplifying y + 1.25 = -4.069705149 Reorder the terms: 1.25 + y = -4.069705149 Solving 1.25 + y = -4.069705149 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + y = -4.069705149 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -4.069705149 + -1.25 y = -4.069705149 + -1.25 Combine like terms: -4.069705149 + -1.25 = -5.319705149 y = -5.319705149 Simplifying y = -5.319705149Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.819705149, -5.319705149}
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