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Simplifying y2 + -14y = -47 Reorder the terms: -14y + y2 = -47 Solving -14y + y2 = -47 Solving for variable 'y'. Reorder the terms: 47 + -14y + y2 = -47 + 47 Combine like terms: -47 + 47 = 0 47 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-47' to each side of the equation. 47 + -14y + -47 + y2 = 0 + -47 Reorder the terms: 47 + -47 + -14y + y2 = 0 + -47 Combine like terms: 47 + -47 = 0 0 + -14y + y2 = 0 + -47 -14y + y2 = 0 + -47 Combine like terms: 0 + -47 = -47 -14y + y2 = -47 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 = -47 + 49 Reorder the terms: 49 + -14y + y2 = -47 + 49 Combine like terms: -47 + 49 = 2 49 + -14y + y2 = 2 Factor a perfect square on the left side: (y + -7)(y + -7) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (y + -7) equal to 1.414213562 and -1.414213562.Subproblem 1
y + -7 = 1.414213562 Simplifying y + -7 = 1.414213562 Reorder the terms: -7 + y = 1.414213562 Solving -7 + y = 1.414213562 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 = 1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + y = 1.414213562 + 7 y = 1.414213562 + 7 Combine like terms: 1.414213562 + 7 = 8.414213562 y = 8.414213562 Simplifying y = 8.414213562Subproblem 2
y + -7 = -1.414213562 Simplifying y + -7 = -1.414213562 Reorder the terms: -7 + y = -1.414213562 Solving -7 + y = -1.414213562 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 = -1.414213562 + 7 Combine like terms: -7 + 7 = 0 0 + y = -1.414213562 + 7 y = -1.414213562 + 7 Combine like terms: -1.414213562 + 7 = 5.585786438 y = 5.585786438 Simplifying y = 5.585786438Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.414213562, 5.585786438}
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