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Simplifying y2 + -12y = -29 Reorder the terms: -12y + y2 = -29 Solving -12y + y2 = -29 Solving for variable 'y'. Reorder the terms: 29 + -12y + y2 = -29 + 29 Combine like terms: -29 + 29 = 0 29 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + -12y + -29 + y2 = 0 + -29 Reorder the terms: 29 + -29 + -12y + y2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -12y + y2 = 0 + -29 -12y + y2 = 0 + -29 Combine like terms: 0 + -29 = -29 -12y + y2 = -29 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = -29 + 36 Reorder the terms: 36 + -12y + y2 = -29 + 36 Combine like terms: -29 + 36 = 7 36 + -12y + y2 = 7 Factor a perfect square on the left side: (y + -6)(y + -6) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -6) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -6 = 2.645751311 Simplifying y + -6 = 2.645751311 Reorder the terms: -6 + y = 2.645751311 Solving -6 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + y = 2.645751311 + 6 y = 2.645751311 + 6 Combine like terms: 2.645751311 + 6 = 8.645751311 y = 8.645751311 Simplifying y = 8.645751311Subproblem 2
y + -6 = -2.645751311 Simplifying y + -6 = -2.645751311 Reorder the terms: -6 + y = -2.645751311 Solving -6 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + y = -2.645751311 + 6 y = -2.645751311 + 6 Combine like terms: -2.645751311 + 6 = 3.354248689 y = 3.354248689 Simplifying y = 3.354248689Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.645751311, 3.354248689}
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