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Simplifying 42u2 + 32u = 9 Reorder the terms: 32u + 42u2 = 9 Solving 32u + 42u2 = 9 Solving for variable 'u'. Reorder the terms: -9 + 32u + 42u2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 32u + 42u2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.2142857143 + 0.7619047619u + u2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.7619047619u + 0.2142857143 + u2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.7619047619u + u2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.7619047619u + u2 = 0 + 0.2142857143 0.7619047619u + u2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.7619047619u + u2 = 0.2142857143 The u term is 0.7619047619u. Take half its coefficient (0.380952381). Square it (0.1451247166) and add it to both sides. Add '0.1451247166' to each side of the equation. 0.7619047619u + 0.1451247166 + u2 = 0.2142857143 + 0.1451247166 Reorder the terms: 0.1451247166 + 0.7619047619u + u2 = 0.2142857143 + 0.1451247166 Combine like terms: 0.2142857143 + 0.1451247166 = 0.3594104309 0.1451247166 + 0.7619047619u + u2 = 0.3594104309 Factor a perfect square on the left side: (u + 0.380952381)(u + 0.380952381) = 0.3594104309 Calculate the square root of the right side: 0.599508491 Break this problem into two subproblems by setting (u + 0.380952381) equal to 0.599508491 and -0.599508491.Subproblem 1
u + 0.380952381 = 0.599508491 Simplifying u + 0.380952381 = 0.599508491 Reorder the terms: 0.380952381 + u = 0.599508491 Solving 0.380952381 + u = 0.599508491 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.380952381' to each side of the equation. 0.380952381 + -0.380952381 + u = 0.599508491 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + u = 0.599508491 + -0.380952381 u = 0.599508491 + -0.380952381 Combine like terms: 0.599508491 + -0.380952381 = 0.21855611 u = 0.21855611 Simplifying u = 0.21855611Subproblem 2
u + 0.380952381 = -0.599508491 Simplifying u + 0.380952381 = -0.599508491 Reorder the terms: 0.380952381 + u = -0.599508491 Solving 0.380952381 + u = -0.599508491 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.380952381' to each side of the equation. 0.380952381 + -0.380952381 + u = -0.599508491 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + u = -0.599508491 + -0.380952381 u = -0.599508491 + -0.380952381 Combine like terms: -0.599508491 + -0.380952381 = -0.980460872 u = -0.980460872 Simplifying u = -0.980460872Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.21855611, -0.980460872}
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