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Simplifying y2 + -14y = -46 Reorder the terms: -14y + y2 = -46 Solving -14y + y2 = -46 Solving for variable 'y'. Reorder the terms: 46 + -14y + y2 = -46 + 46 Combine like terms: -46 + 46 = 0 46 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -14y + -46 + y2 = 0 + -46 Reorder the terms: 46 + -46 + -14y + y2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -14y + y2 = 0 + -46 -14y + y2 = 0 + -46 Combine like terms: 0 + -46 = -46 -14y + y2 = -46 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 = -46 + 49 Reorder the terms: 49 + -14y + y2 = -46 + 49 Combine like terms: -46 + 49 = 3 49 + -14y + y2 = 3 Factor a perfect square on the left side: (y + -7)(y + -7) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (y + -7) equal to 1.732050808 and -1.732050808.Subproblem 1
y + -7 = 1.732050808 Simplifying y + -7 = 1.732050808 Reorder the terms: -7 + y = 1.732050808 Solving -7 + y = 1.732050808 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 = 1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + y = 1.732050808 + 7 y = 1.732050808 + 7 Combine like terms: 1.732050808 + 7 = 8.732050808 y = 8.732050808 Simplifying y = 8.732050808Subproblem 2
y + -7 = -1.732050808 Simplifying y + -7 = -1.732050808 Reorder the terms: -7 + y = -1.732050808 Solving -7 + y = -1.732050808 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 = -1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + y = -1.732050808 + 7 y = -1.732050808 + 7 Combine like terms: -1.732050808 + 7 = 5.267949192 y = 5.267949192 Simplifying y = 5.267949192Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.732050808, 5.267949192}
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