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Simplifying 9y2 + -29y + 12 = 0 Reorder the terms: 12 + -29y + 9y2 = 0 Solving 12 + -29y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.333333333 + -3.222222222y + y2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -3.222222222y + -1.333333333 + y2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -3.222222222y + y2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -3.222222222y + y2 = 0 + -1.333333333 -3.222222222y + y2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -3.222222222y + y2 = -1.333333333 The y term is -3.222222222y. Take half its coefficient (-1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. -3.222222222y + 2.595679012 + y2 = -1.333333333 + 2.595679012 Reorder the terms: 2.595679012 + -3.222222222y + y2 = -1.333333333 + 2.595679012 Combine like terms: -1.333333333 + 2.595679012 = 1.262345679 2.595679012 + -3.222222222y + y2 = 1.262345679 Factor a perfect square on the left side: (y + -1.611111111)(y + -1.611111111) = 1.262345679 Calculate the square root of the right side: 1.123541579 Break this problem into two subproblems by setting (y + -1.611111111) equal to 1.123541579 and -1.123541579.Subproblem 1
y + -1.611111111 = 1.123541579 Simplifying y + -1.611111111 = 1.123541579 Reorder the terms: -1.611111111 + y = 1.123541579 Solving -1.611111111 + y = 1.123541579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + y = 1.123541579 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = 1.123541579 + 1.611111111 y = 1.123541579 + 1.611111111 Combine like terms: 1.123541579 + 1.611111111 = 2.73465269 y = 2.73465269 Simplifying y = 2.73465269Subproblem 2
y + -1.611111111 = -1.123541579 Simplifying y + -1.611111111 = -1.123541579 Reorder the terms: -1.611111111 + y = -1.123541579 Solving -1.611111111 + y = -1.123541579 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + y = -1.123541579 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = -1.123541579 + 1.611111111 y = -1.123541579 + 1.611111111 Combine like terms: -1.123541579 + 1.611111111 = 0.487569532 y = 0.487569532 Simplifying y = 0.487569532Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.73465269, 0.487569532}
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