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Simplifying y2 + 14 = 18y Reorder the terms: 14 + y2 = 18y Solving 14 + y2 = 18y Solving for variable 'y'. Reorder the terms: 14 + -18y + y2 = 18y + -18y Combine like terms: 18y + -18y = 0 14 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -18y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -18y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -18y + y2 = 0 + -14 -18y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -18y + y2 = -14 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = -14 + 81 Reorder the terms: 81 + -18y + y2 = -14 + 81 Combine like terms: -14 + 81 = 67 81 + -18y + y2 = 67 Factor a perfect square on the left side: (y + -9)(y + -9) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (y + -9) equal to 8.185352772 and -8.185352772.Subproblem 1
y + -9 = 8.185352772 Simplifying y + -9 = 8.185352772 Reorder the terms: -9 + y = 8.185352772 Solving -9 + y = 8.185352772 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + y = 8.185352772 + 9 y = 8.185352772 + 9 Combine like terms: 8.185352772 + 9 = 17.185352772 y = 17.185352772 Simplifying y = 17.185352772Subproblem 2
y + -9 = -8.185352772 Simplifying y + -9 = -8.185352772 Reorder the terms: -9 + y = -8.185352772 Solving -9 + y = -8.185352772 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + y = -8.185352772 + 9 y = -8.185352772 + 9 Combine like terms: -8.185352772 + 9 = 0.814647228 y = 0.814647228 Simplifying y = 0.814647228Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.185352772, 0.814647228}
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