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Simplifying 2u2 + -13u + 5 = 0 Reorder the terms: 5 + -13u + 2u2 = 0 Solving 5 + -13u + 2u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -6.5u + u2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -6.5u + -2.5 + u2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -6.5u + u2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -6.5u + u2 = 0 + -2.5 -6.5u + u2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -6.5u + u2 = -2.5 The u term is -6.5u. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5u + 10.5625 + u2 = -2.5 + 10.5625 Reorder the terms: 10.5625 + -6.5u + u2 = -2.5 + 10.5625 Combine like terms: -2.5 + 10.5625 = 8.0625 10.5625 + -6.5u + u2 = 8.0625 Factor a perfect square on the left side: (u + -3.25)(u + -3.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (u + -3.25) equal to 2.839454173 and -2.839454173.Subproblem 1
u + -3.25 = 2.839454173 Simplifying u + -3.25 = 2.839454173 Reorder the terms: -3.25 + u = 2.839454173 Solving -3.25 + u = 2.839454173 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + u = 2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + u = 2.839454173 + 3.25 u = 2.839454173 + 3.25 Combine like terms: 2.839454173 + 3.25 = 6.089454173 u = 6.089454173 Simplifying u = 6.089454173Subproblem 2
u + -3.25 = -2.839454173 Simplifying u + -3.25 = -2.839454173 Reorder the terms: -3.25 + u = -2.839454173 Solving -3.25 + u = -2.839454173 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + u = -2.839454173 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + u = -2.839454173 + 3.25 u = -2.839454173 + 3.25 Combine like terms: -2.839454173 + 3.25 = 0.410545827 u = 0.410545827 Simplifying u = 0.410545827Solution
The solution to the problem is based on the solutions from the subproblems. u = {6.089454173, 0.410545827}
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