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Simplifying y2 + 42 = 14y Reorder the terms: 42 + y2 = 14y Solving 42 + y2 = 14y Solving for variable 'y'. Reorder the terms: 42 + -14y + y2 = 14y + -14y Combine like terms: 14y + -14y = 0 42 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -14y + -42 + y2 = 0 + -42 Reorder the terms: 42 + -42 + -14y + y2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -14y + y2 = 0 + -42 -14y + y2 = 0 + -42 Combine like terms: 0 + -42 = -42 -14y + y2 = -42 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = -42 + 49 Reorder the terms: 49 + -14y + y2 = -42 + 49 Combine like terms: -42 + 49 = 7 49 + -14y + y2 = 7 Factor a perfect square on the left side: (y + -7)(y + -7) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (y + -7) equal to 2.645751311 and -2.645751311.Subproblem 1
y + -7 = 2.645751311 Simplifying y + -7 = 2.645751311 Reorder the terms: -7 + y = 2.645751311 Solving -7 + y = 2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + y = 2.645751311 + 7 y = 2.645751311 + 7 Combine like terms: 2.645751311 + 7 = 9.645751311 y = 9.645751311 Simplifying y = 9.645751311Subproblem 2
y + -7 = -2.645751311 Simplifying y + -7 = -2.645751311 Reorder the terms: -7 + y = -2.645751311 Solving -7 + y = -2.645751311 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -2.645751311 + 7 Combine like terms: -7 + 7 = 0 0 + y = -2.645751311 + 7 y = -2.645751311 + 7 Combine like terms: -2.645751311 + 7 = 4.354248689 y = 4.354248689 Simplifying y = 4.354248689Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.645751311, 4.354248689}
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