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Simplifying 5u2 + 41u + -42 = 0 Reorder the terms: -42 + 41u + 5u2 = 0 Solving -42 + 41u + 5u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.4 + 8.2u + u2 = 0 Move the constant term to the right: Add '8.4' to each side of the equation. -8.4 + 8.2u + 8.4 + u2 = 0 + 8.4 Reorder the terms: -8.4 + 8.4 + 8.2u + u2 = 0 + 8.4 Combine like terms: -8.4 + 8.4 = 0.0 0.0 + 8.2u + u2 = 0 + 8.4 8.2u + u2 = 0 + 8.4 Combine like terms: 0 + 8.4 = 8.4 8.2u + u2 = 8.4 The u term is 8.2u. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2u + 16.81 + u2 = 8.4 + 16.81 Reorder the terms: 16.81 + 8.2u + u2 = 8.4 + 16.81 Combine like terms: 8.4 + 16.81 = 25.21 16.81 + 8.2u + u2 = 25.21 Factor a perfect square on the left side: (u + 4.1)(u + 4.1) = 25.21 Calculate the square root of the right side: 5.020956084 Break this problem into two subproblems by setting (u + 4.1) equal to 5.020956084 and -5.020956084.Subproblem 1
u + 4.1 = 5.020956084 Simplifying u + 4.1 = 5.020956084 Reorder the terms: 4.1 + u = 5.020956084 Solving 4.1 + u = 5.020956084 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + u = 5.020956084 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + u = 5.020956084 + -4.1 u = 5.020956084 + -4.1 Combine like terms: 5.020956084 + -4.1 = 0.920956084 u = 0.920956084 Simplifying u = 0.920956084Subproblem 2
u + 4.1 = -5.020956084 Simplifying u + 4.1 = -5.020956084 Reorder the terms: 4.1 + u = -5.020956084 Solving 4.1 + u = -5.020956084 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + u = -5.020956084 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + u = -5.020956084 + -4.1 u = -5.020956084 + -4.1 Combine like terms: -5.020956084 + -4.1 = -9.120956084 u = -9.120956084 Simplifying u = -9.120956084Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.920956084, -9.120956084}
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