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Simplifying 11y(y + 2) + -3 = 29 Reorder the terms: 11y(2 + y) + -3 = 29 (2 * 11y + y * 11y) + -3 = 29 (22y + 11y2) + -3 = 29 Reorder the terms: -3 + 22y + 11y2 = 29 Solving -3 + 22y + 11y2 = 29 Solving for variable 'y'. Reorder the terms: -3 + -29 + 22y + 11y2 = 29 + -29 Combine like terms: -3 + -29 = -32 -32 + 22y + 11y2 = 29 + -29 Combine like terms: 29 + -29 = 0 -32 + 22y + 11y2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -2.909090909 + 2y + y2 = 0 Move the constant term to the right: Add '2.909090909' to each side of the equation. -2.909090909 + 2y + 2.909090909 + y2 = 0 + 2.909090909 Reorder the terms: -2.909090909 + 2.909090909 + 2y + y2 = 0 + 2.909090909 Combine like terms: -2.909090909 + 2.909090909 = 0.000000000 0.000000000 + 2y + y2 = 0 + 2.909090909 2y + y2 = 0 + 2.909090909 Combine like terms: 0 + 2.909090909 = 2.909090909 2y + y2 = 2.909090909 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 2.909090909 + 1 Reorder the terms: 1 + 2y + y2 = 2.909090909 + 1 Combine like terms: 2.909090909 + 1 = 3.909090909 1 + 2y + y2 = 3.909090909 Factor a perfect square on the left side: (y + 1)(y + 1) = 3.909090909 Calculate the square root of the right side: 1.977142106 Break this problem into two subproblems by setting (y + 1) equal to 1.977142106 and -1.977142106.Subproblem 1
y + 1 = 1.977142106 Simplifying y + 1 = 1.977142106 Reorder the terms: 1 + y = 1.977142106 Solving 1 + y = 1.977142106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 1.977142106 + -1 Combine like terms: 1 + -1 = 0 0 + y = 1.977142106 + -1 y = 1.977142106 + -1 Combine like terms: 1.977142106 + -1 = 0.977142106 y = 0.977142106 Simplifying y = 0.977142106Subproblem 2
y + 1 = -1.977142106 Simplifying y + 1 = -1.977142106 Reorder the terms: 1 + y = -1.977142106 Solving 1 + y = -1.977142106 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -1.977142106 + -1 Combine like terms: 1 + -1 = 0 0 + y = -1.977142106 + -1 y = -1.977142106 + -1 Combine like terms: -1.977142106 + -1 = -2.977142106 y = -2.977142106 Simplifying y = -2.977142106Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.977142106, -2.977142106}
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