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Simplifying 7(Y + 7) * Y = 6 Reorder the terms: 7(7 + Y) * Y = 6 Reorder the terms for easier multiplication: 7Y(7 + Y) = 6 (7 * 7Y + Y * 7Y) = 6 (49Y + 7Y2) = 6 Solving 49Y + 7Y2 = 6 Solving for variable 'Y'. Reorder the terms: -6 + 49Y + 7Y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 49Y + 7Y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 7Y + Y2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 7Y + 0.8571428571 + Y2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 7Y + Y2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 7Y + Y2 = 0 + 0.8571428571 7Y + Y2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 7Y + Y2 = 0.8571428571 The Y term is 7Y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7Y + 12.25 + Y2 = 0.8571428571 + 12.25 Reorder the terms: 12.25 + 7Y + Y2 = 0.8571428571 + 12.25 Combine like terms: 0.8571428571 + 12.25 = 13.1071428571 12.25 + 7Y + Y2 = 13.1071428571 Factor a perfect square on the left side: (Y + 3.5)(Y + 3.5) = 13.1071428571 Calculate the square root of the right side: 3.620378828 Break this problem into two subproblems by setting (Y + 3.5) equal to 3.620378828 and -3.620378828.Subproblem 1
Y + 3.5 = 3.620378828 Simplifying Y + 3.5 = 3.620378828 Reorder the terms: 3.5 + Y = 3.620378828 Solving 3.5 + Y = 3.620378828 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + Y = 3.620378828 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + Y = 3.620378828 + -3.5 Y = 3.620378828 + -3.5 Combine like terms: 3.620378828 + -3.5 = 0.120378828 Y = 0.120378828 Simplifying Y = 0.120378828Subproblem 2
Y + 3.5 = -3.620378828 Simplifying Y + 3.5 = -3.620378828 Reorder the terms: 3.5 + Y = -3.620378828 Solving 3.5 + Y = -3.620378828 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + Y = -3.620378828 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + Y = -3.620378828 + -3.5 Y = -3.620378828 + -3.5 Combine like terms: -3.620378828 + -3.5 = -7.120378828 Y = -7.120378828 Simplifying Y = -7.120378828Solution
The solution to the problem is based on the solutions from the subproblems. Y = {0.120378828, -7.120378828}
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