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Simplifying y + 2y(y + -5) = 2y + 2 Reorder the terms: y + 2y(-5 + y) = 2y + 2 y + (-5 * 2y + y * 2y) = 2y + 2 y + (-10y + 2y2) = 2y + 2 Combine like terms: y + -10y = -9y -9y + 2y2 = 2y + 2 Reorder the terms: -9y + 2y2 = 2 + 2y Solving -9y + 2y2 = 2 + 2y Solving for variable 'y'. Reorder the terms: -2 + -9y + -2y + 2y2 = 2 + 2y + -2 + -2y Combine like terms: -9y + -2y = -11y -2 + -11y + 2y2 = 2 + 2y + -2 + -2y Reorder the terms: -2 + -11y + 2y2 = 2 + -2 + 2y + -2y Combine like terms: 2 + -2 = 0 -2 + -11y + 2y2 = 0 + 2y + -2y -2 + -11y + 2y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -2 + -11y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -5.5y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -5.5y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -5.5y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5.5y + y2 = 0 + 1 -5.5y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5.5y + y2 = 1 The y term is -5.5y. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5y + 7.5625 + y2 = 1 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = 1 + 7.5625 Combine like terms: 1 + 7.5625 = 8.5625 7.5625 + -5.5y + y2 = 8.5625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 8.5625 Calculate the square root of the right side: 2.926174978 Break this problem into two subproblems by setting (y + -2.75) equal to 2.926174978 and -2.926174978.Subproblem 1
y + -2.75 = 2.926174978 Simplifying y + -2.75 = 2.926174978 Reorder the terms: -2.75 + y = 2.926174978 Solving -2.75 + y = 2.926174978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 2.926174978 + 2.75 y = 2.926174978 + 2.75 Combine like terms: 2.926174978 + 2.75 = 5.676174978 y = 5.676174978 Simplifying y = 5.676174978Subproblem 2
y + -2.75 = -2.926174978 Simplifying y + -2.75 = -2.926174978 Reorder the terms: -2.75 + y = -2.926174978 Solving -2.75 + y = -2.926174978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -2.926174978 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -2.926174978 + 2.75 y = -2.926174978 + 2.75 Combine like terms: -2.926174978 + 2.75 = -0.176174978 y = -0.176174978 Simplifying y = -0.176174978Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.676174978, -0.176174978}
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