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Simplifying 2y2 + 5y = 5 Reorder the terms: 5y + 2y2 = 5 Solving 5y + 2y2 = 5 Solving for variable 'y'. Reorder the terms: -5 + 5y + 2y2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 2.5y + y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.5y + 2.5 + y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.5y + y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.5y + y2 = 0 + 2.5 2.5y + y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.5y + y2 = 2.5 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 = 2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = 2.5 + 1.5625 Combine like terms: 2.5 + 1.5625 = 4.0625 1.5625 + 2.5y + y2 = 4.0625 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = 4.0625 Calculate the square root of the right side: 2.015564437 Break this problem into two subproblems by setting (y + 1.25) equal to 2.015564437 and -2.015564437.Subproblem 1
y + 1.25 = 2.015564437 Simplifying y + 1.25 = 2.015564437 Reorder the terms: 1.25 + y = 2.015564437 Solving 1.25 + y = 2.015564437 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 = 2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 2.015564437 + -1.25 y = 2.015564437 + -1.25 Combine like terms: 2.015564437 + -1.25 = 0.765564437 y = 0.765564437 Simplifying y = 0.765564437Subproblem 2
y + 1.25 = -2.015564437 Simplifying y + 1.25 = -2.015564437 Reorder the terms: 1.25 + y = -2.015564437 Solving 1.25 + y = -2.015564437 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 = -2.015564437 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -2.015564437 + -1.25 y = -2.015564437 + -1.25 Combine like terms: -2.015564437 + -1.25 = -3.265564437 y = -3.265564437 Simplifying y = -3.265564437Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.765564437, -3.265564437}
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