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Simplifying u2 + 6u2 = 4u + 24 Combine like terms: u2 + 6u2 = 7u2 7u2 = 4u + 24 Reorder the terms: 7u2 = 24 + 4u Solving 7u2 = 24 + 4u Solving for variable 'u'. Reorder the terms: -24 + -4u + 7u2 = 24 + 4u + -24 + -4u Reorder the terms: -24 + -4u + 7u2 = 24 + -24 + 4u + -4u Combine like terms: 24 + -24 = 0 -24 + -4u + 7u2 = 0 + 4u + -4u -24 + -4u + 7u2 = 4u + -4u Combine like terms: 4u + -4u = 0 -24 + -4u + 7u2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.428571429 + -0.5714285714u + u2 = 0 Move the constant term to the right: Add '3.428571429' to each side of the equation. -3.428571429 + -0.5714285714u + 3.428571429 + u2 = 0 + 3.428571429 Reorder the terms: -3.428571429 + 3.428571429 + -0.5714285714u + u2 = 0 + 3.428571429 Combine like terms: -3.428571429 + 3.428571429 = 0.000000000 0.000000000 + -0.5714285714u + u2 = 0 + 3.428571429 -0.5714285714u + u2 = 0 + 3.428571429 Combine like terms: 0 + 3.428571429 = 3.428571429 -0.5714285714u + u2 = 3.428571429 The u term is -0.5714285714u. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714u + 0.08163265305 + u2 = 3.428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714u + u2 = 3.428571429 + 0.08163265305 Combine like terms: 3.428571429 + 0.08163265305 = 3.51020408205 0.08163265305 + -0.5714285714u + u2 = 3.51020408205 Factor a perfect square on the left side: (u + -0.2857142857)(u + -0.2857142857) = 3.51020408205 Calculate the square root of the right side: 1.873553864 Break this problem into two subproblems by setting (u + -0.2857142857) equal to 1.873553864 and -1.873553864.Subproblem 1
u + -0.2857142857 = 1.873553864 Simplifying u + -0.2857142857 = 1.873553864 Reorder the terms: -0.2857142857 + u = 1.873553864 Solving -0.2857142857 + u = 1.873553864 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + u = 1.873553864 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + u = 1.873553864 + 0.2857142857 u = 1.873553864 + 0.2857142857 Combine like terms: 1.873553864 + 0.2857142857 = 2.1592681497 u = 2.1592681497 Simplifying u = 2.1592681497Subproblem 2
u + -0.2857142857 = -1.873553864 Simplifying u + -0.2857142857 = -1.873553864 Reorder the terms: -0.2857142857 + u = -1.873553864 Solving -0.2857142857 + u = -1.873553864 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + u = -1.873553864 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + u = -1.873553864 + 0.2857142857 u = -1.873553864 + 0.2857142857 Combine like terms: -1.873553864 + 0.2857142857 = -1.5878395783 u = -1.5878395783 Simplifying u = -1.5878395783Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.1592681497, -1.5878395783}
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