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Simplifying -2y2 + -5y = -10 Reorder the terms: -5y + -2y2 = -10 Solving -5y + -2y2 = -10 Solving for variable 'y'. Reorder the terms: 10 + -5y + -2y2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -5y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -5 + 2.5y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.5y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 2.5y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.5y + y2 = 0 + 5 2.5y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.5y + y2 = 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 = 5 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = 5 + 1.5625 Combine like terms: 5 + 1.5625 = 6.5625 1.5625 + 2.5y + y2 = 6.5625 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (y + 1.25) equal to 2.561737691 and -2.561737691.Subproblem 1
y + 1.25 = 2.561737691 Simplifying y + 1.25 = 2.561737691 Reorder the terms: 1.25 + y = 2.561737691 Solving 1.25 + y = 2.561737691 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 = 2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = 2.561737691 + -1.25 y = 2.561737691 + -1.25 Combine like terms: 2.561737691 + -1.25 = 1.311737691 y = 1.311737691 Simplifying y = 1.311737691Subproblem 2
y + 1.25 = -2.561737691 Simplifying y + 1.25 = -2.561737691 Reorder the terms: 1.25 + y = -2.561737691 Solving 1.25 + y = -2.561737691 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 = -2.561737691 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + y = -2.561737691 + -1.25 y = -2.561737691 + -1.25 Combine like terms: -2.561737691 + -1.25 = -3.811737691 y = -3.811737691 Simplifying y = -3.811737691Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.311737691, -3.811737691}
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