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Simplifying 9y2 + -58y + 21 = 0 Reorder the terms: 21 + -58y + 9y2 = 0 Solving 21 + -58y + 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'. 2.333333333 + -6.444444444y + y2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -6.444444444y + -2.333333333 + y2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -6.444444444y + y2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -6.444444444y + y2 = 0 + -2.333333333 -6.444444444y + y2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -6.444444444y + y2 = -2.333333333 The y term is -6.444444444y. Take half its coefficient (-3.222222222). Square it (10.38271605) and add it to both sides. Add '10.38271605' to each side of the equation. -6.444444444y + 10.38271605 + y2 = -2.333333333 + 10.38271605 Reorder the terms: 10.38271605 + -6.444444444y + y2 = -2.333333333 + 10.38271605 Combine like terms: -2.333333333 + 10.38271605 = 8.049382717 10.38271605 + -6.444444444y + y2 = 8.049382717 Factor a perfect square on the left side: (y + -3.222222222)(y + -3.222222222) = 8.049382717 Calculate the square root of the right side: 2.837143408 Break this problem into two subproblems by setting (y + -3.222222222) equal to 2.837143408 and -2.837143408.Subproblem 1
y + -3.222222222 = 2.837143408 Simplifying y + -3.222222222 = 2.837143408 Reorder the terms: -3.222222222 + y = 2.837143408 Solving -3.222222222 + y = 2.837143408 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + y = 2.837143408 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + y = 2.837143408 + 3.222222222 y = 2.837143408 + 3.222222222 Combine like terms: 2.837143408 + 3.222222222 = 6.05936563 y = 6.05936563 Simplifying y = 6.05936563Subproblem 2
y + -3.222222222 = -2.837143408 Simplifying y + -3.222222222 = -2.837143408 Reorder the terms: -3.222222222 + y = -2.837143408 Solving -3.222222222 + y = -2.837143408 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.222222222' to each side of the equation. -3.222222222 + 3.222222222 + y = -2.837143408 + 3.222222222 Combine like terms: -3.222222222 + 3.222222222 = 0.000000000 0.000000000 + y = -2.837143408 + 3.222222222 y = -2.837143408 + 3.222222222 Combine like terms: -2.837143408 + 3.222222222 = 0.385078814 y = 0.385078814 Simplifying y = 0.385078814Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.05936563, 0.385078814}
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