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Simplifying 11y(2 + -1y) = 2(y + 1) (2 * 11y + -1y * 11y) = 2(y + 1) (22y + -11y2) = 2(y + 1) Reorder the terms: 22y + -11y2 = 2(1 + y) 22y + -11y2 = (1 * 2 + y * 2) 22y + -11y2 = (2 + 2y) Solving 22y + -11y2 = 2 + 2y Solving for variable 'y'. Reorder the terms: -2 + 22y + -2y + -11y2 = 2 + 2y + -2 + -2y Combine like terms: 22y + -2y = 20y -2 + 20y + -11y2 = 2 + 2y + -2 + -2y Reorder the terms: -2 + 20y + -11y2 = 2 + -2 + 2y + -2y Combine like terms: 2 + -2 = 0 -2 + 20y + -11y2 = 0 + 2y + -2y -2 + 20y + -11y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -2 + 20y + -11y2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. 0.1818181818 + -1.818181818y + y2 = 0 Move the constant term to the right: Add '-0.1818181818' to each side of the equation. 0.1818181818 + -1.818181818y + -0.1818181818 + y2 = 0 + -0.1818181818 Reorder the terms: 0.1818181818 + -0.1818181818 + -1.818181818y + y2 = 0 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + -1.818181818y + y2 = 0 + -0.1818181818 -1.818181818y + y2 = 0 + -0.1818181818 Combine like terms: 0 + -0.1818181818 = -0.1818181818 -1.818181818y + y2 = -0.1818181818 The y term is -1.818181818y. Take half its coefficient (-0.909090909). Square it (0.8264462808) and add it to both sides. Add '0.8264462808' to each side of the equation. -1.818181818y + 0.8264462808 + y2 = -0.1818181818 + 0.8264462808 Reorder the terms: 0.8264462808 + -1.818181818y + y2 = -0.1818181818 + 0.8264462808 Combine like terms: -0.1818181818 + 0.8264462808 = 0.644628099 0.8264462808 + -1.818181818y + y2 = 0.644628099 Factor a perfect square on the left side: (y + -0.909090909)(y + -0.909090909) = 0.644628099 Calculate the square root of the right side: 0.802887351 Break this problem into two subproblems by setting (y + -0.909090909) equal to 0.802887351 and -0.802887351.Subproblem 1
y + -0.909090909 = 0.802887351 Simplifying y + -0.909090909 = 0.802887351 Reorder the terms: -0.909090909 + y = 0.802887351 Solving -0.909090909 + y = 0.802887351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + y = 0.802887351 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + y = 0.802887351 + 0.909090909 y = 0.802887351 + 0.909090909 Combine like terms: 0.802887351 + 0.909090909 = 1.71197826 y = 1.71197826 Simplifying y = 1.71197826Subproblem 2
y + -0.909090909 = -0.802887351 Simplifying y + -0.909090909 = -0.802887351 Reorder the terms: -0.909090909 + y = -0.802887351 Solving -0.909090909 + y = -0.802887351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.909090909' to each side of the equation. -0.909090909 + 0.909090909 + y = -0.802887351 + 0.909090909 Combine like terms: -0.909090909 + 0.909090909 = 0.000000000 0.000000000 + y = -0.802887351 + 0.909090909 y = -0.802887351 + 0.909090909 Combine like terms: -0.802887351 + 0.909090909 = 0.106203558 y = 0.106203558 Simplifying y = 0.106203558Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.71197826, 0.106203558}
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