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Simplifying 4(Y + 6) * 7Y = 3 Reorder the terms: 4(6 + Y) * 7Y = 3 Reorder the terms for easier multiplication: 4 * 7Y(6 + Y) = 3 Multiply 4 * 7 28Y(6 + Y) = 3 (6 * 28Y + Y * 28Y) = 3 (168Y + 28Y2) = 3 Solving 168Y + 28Y2 = 3 Solving for variable 'Y'. Reorder the terms: -3 + 168Y + 28Y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 168Y + 28Y2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.1071428571 + 6Y + Y2 = 0 Move the constant term to the right: Add '0.1071428571' to each side of the equation. -0.1071428571 + 6Y + 0.1071428571 + Y2 = 0 + 0.1071428571 Reorder the terms: -0.1071428571 + 0.1071428571 + 6Y + Y2 = 0 + 0.1071428571 Combine like terms: -0.1071428571 + 0.1071428571 = 0.0000000000 0.0000000000 + 6Y + Y2 = 0 + 0.1071428571 6Y + Y2 = 0 + 0.1071428571 Combine like terms: 0 + 0.1071428571 = 0.1071428571 6Y + Y2 = 0.1071428571 The Y term is 6Y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6Y + 9 + Y2 = 0.1071428571 + 9 Reorder the terms: 9 + 6Y + Y2 = 0.1071428571 + 9 Combine like terms: 0.1071428571 + 9 = 9.1071428571 9 + 6Y + Y2 = 9.1071428571 Factor a perfect square on the left side: (Y + 3)(Y + 3) = 9.1071428571 Calculate the square root of the right side: 3.017804311 Break this problem into two subproblems by setting (Y + 3) equal to 3.017804311 and -3.017804311.Subproblem 1
Y + 3 = 3.017804311 Simplifying Y + 3 = 3.017804311 Reorder the terms: 3 + Y = 3.017804311 Solving 3 + Y = 3.017804311 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Y = 3.017804311 + -3 Combine like terms: 3 + -3 = 0 0 + Y = 3.017804311 + -3 Y = 3.017804311 + -3 Combine like terms: 3.017804311 + -3 = 0.017804311 Y = 0.017804311 Simplifying Y = 0.017804311Subproblem 2
Y + 3 = -3.017804311 Simplifying Y + 3 = -3.017804311 Reorder the terms: 3 + Y = -3.017804311 Solving 3 + Y = -3.017804311 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + Y = -3.017804311 + -3 Combine like terms: 3 + -3 = 0 0 + Y = -3.017804311 + -3 Y = -3.017804311 + -3 Combine like terms: -3.017804311 + -3 = -6.017804311 Y = -6.017804311 Simplifying Y = -6.017804311Solution
The solution to the problem is based on the solutions from the subproblems. Y = {0.017804311, -6.017804311}
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