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Simplifying 9y2 + -36y + -134 = 0 Reorder the terms: -134 + -36y + 9y2 = 0 Solving -134 + -36y + 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'. -14.88888889 + -4y + y2 = 0 Move the constant term to the right: Add '14.88888889' to each side of the equation. -14.88888889 + -4y + 14.88888889 + y2 = 0 + 14.88888889 Reorder the terms: -14.88888889 + 14.88888889 + -4y + y2 = 0 + 14.88888889 Combine like terms: -14.88888889 + 14.88888889 = 0.00000000 0.00000000 + -4y + y2 = 0 + 14.88888889 -4y + y2 = 0 + 14.88888889 Combine like terms: 0 + 14.88888889 = 14.88888889 -4y + y2 = 14.88888889 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 14.88888889 + 4 Reorder the terms: 4 + -4y + y2 = 14.88888889 + 4 Combine like terms: 14.88888889 + 4 = 18.88888889 4 + -4y + y2 = 18.88888889 Factor a perfect square on the left side: (y + -2)(y + -2) = 18.88888889 Calculate the square root of the right side: 4.346134937 Break this problem into two subproblems by setting (y + -2) equal to 4.346134937 and -4.346134937.Subproblem 1
y + -2 = 4.346134937 Simplifying y + -2 = 4.346134937 Reorder the terms: -2 + y = 4.346134937 Solving -2 + y = 4.346134937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 4.346134937 + 2 Combine like terms: -2 + 2 = 0 0 + y = 4.346134937 + 2 y = 4.346134937 + 2 Combine like terms: 4.346134937 + 2 = 6.346134937 y = 6.346134937 Simplifying y = 6.346134937Subproblem 2
y + -2 = -4.346134937 Simplifying y + -2 = -4.346134937 Reorder the terms: -2 + y = -4.346134937 Solving -2 + y = -4.346134937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -4.346134937 + 2 Combine like terms: -2 + 2 = 0 0 + y = -4.346134937 + 2 y = -4.346134937 + 2 Combine like terms: -4.346134937 + 2 = -2.346134937 y = -2.346134937 Simplifying y = -2.346134937Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.346134937, -2.346134937}
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