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Simplifying y2 + 12y = 35 Reorder the terms: 12y + y2 = 35 Solving 12y + y2 = 35 Solving for variable 'y'. Reorder the terms: -35 + 12y + y2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 12y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + 12y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 12y + y2 = 0 + 35 12y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 12y + y2 = 35 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 = 35 + 36 Reorder the terms: 36 + 12y + y2 = 35 + 36 Combine like terms: 35 + 36 = 71 36 + 12y + y2 = 71 Factor a perfect square on the left side: (y + 6)(y + 6) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (y + 6) equal to 8.426149773 and -8.426149773.Subproblem 1
y + 6 = 8.426149773 Simplifying y + 6 = 8.426149773 Reorder the terms: 6 + y = 8.426149773 Solving 6 + y = 8.426149773 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 = 8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + y = 8.426149773 + -6 y = 8.426149773 + -6 Combine like terms: 8.426149773 + -6 = 2.426149773 y = 2.426149773 Simplifying y = 2.426149773Subproblem 2
y + 6 = -8.426149773 Simplifying y + 6 = -8.426149773 Reorder the terms: 6 + y = -8.426149773 Solving 6 + y = -8.426149773 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 = -8.426149773 + -6 Combine like terms: 6 + -6 = 0 0 + y = -8.426149773 + -6 y = -8.426149773 + -6 Combine like terms: -8.426149773 + -6 = -14.426149773 y = -14.426149773 Simplifying y = -14.426149773Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.426149773, -14.426149773}
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