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Simplifying 2y2 + 7y = 7 Reorder the terms: 7y + 2y2 = 7 Solving 7y + 2y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + 7y + 2y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 7y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 3.5y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 3.5y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 3.5y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 3.5y + y2 = 0 + 3.5 3.5y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 3.5y + y2 = 3.5 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = 3.5 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = 3.5 + 3.0625 Combine like terms: 3.5 + 3.0625 = 6.5625 3.0625 + 3.5y + y2 = 6.5625 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (y + 1.75) equal to 2.561737691 and -2.561737691.Subproblem 1
y + 1.75 = 2.561737691 Simplifying y + 1.75 = 2.561737691 Reorder the terms: 1.75 + y = 2.561737691 Solving 1.75 + y = 2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = 2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = 2.561737691 + -1.75 y = 2.561737691 + -1.75 Combine like terms: 2.561737691 + -1.75 = 0.811737691 y = 0.811737691 Simplifying y = 0.811737691Subproblem 2
y + 1.75 = -2.561737691 Simplifying y + 1.75 = -2.561737691 Reorder the terms: 1.75 + y = -2.561737691 Solving 1.75 + y = -2.561737691 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + y = -2.561737691 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + y = -2.561737691 + -1.75 y = -2.561737691 + -1.75 Combine like terms: -2.561737691 + -1.75 = -4.311737691 y = -4.311737691 Simplifying y = -4.311737691Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.811737691, -4.311737691}
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