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Simplifying y2 + 12y + 36 = 7 Reorder the terms: 36 + 12y + y2 = 7 Solving 36 + 12y + y2 = 7 Solving for variable 'y'. Reorder the terms: 36 + -7 + 12y + y2 = 7 + -7 Combine like terms: 36 + -7 = 29 29 + 12y + y2 = 7 + -7 Combine like terms: 7 + -7 = 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 = -3.354248689 y = -3.354248689 Simplifying y = -3.354248689Subproblem 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 = -8.645751311 y = -8.645751311 Simplifying y = -8.645751311Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.354248689, -8.645751311}
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