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Simplifying Y2 + 14Y + 8 = 0 Reorder the terms: 8 + 14Y + Y2 = 0 Solving 8 + 14Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 14Y + -8 + Y2 = 0 + -8 Reorder the terms: 8 + -8 + 14Y + Y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 14Y + Y2 = 0 + -8 14Y + Y2 = 0 + -8 Combine like terms: 0 + -8 = -8 14Y + Y2 = -8 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 = -8 + 49 Reorder the terms: 49 + 14Y + Y2 = -8 + 49 Combine like terms: -8 + 49 = 41 49 + 14Y + Y2 = 41 Factor a perfect square on the left side: (Y + 7)(Y + 7) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (Y + 7) equal to 6.403124237 and -6.403124237.Subproblem 1
Y + 7 = 6.403124237 Simplifying Y + 7 = 6.403124237 Reorder the terms: 7 + Y = 6.403124237 Solving 7 + Y = 6.403124237 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 = 6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + Y = 6.403124237 + -7 Y = 6.403124237 + -7 Combine like terms: 6.403124237 + -7 = -0.596875763 Y = -0.596875763 Simplifying Y = -0.596875763Subproblem 2
Y + 7 = -6.403124237 Simplifying Y + 7 = -6.403124237 Reorder the terms: 7 + Y = -6.403124237 Solving 7 + Y = -6.403124237 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 = -6.403124237 + -7 Combine like terms: 7 + -7 = 0 0 + Y = -6.403124237 + -7 Y = -6.403124237 + -7 Combine like terms: -6.403124237 + -7 = -13.403124237 Y = -13.403124237 Simplifying Y = -13.403124237Solution
The solution to the problem is based on the solutions from the subproblems. Y = {-0.596875763, -13.403124237}
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