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Simplifying 3u2 + 18u + -77 = 0 Reorder the terms: -77 + 18u + 3u2 = 0 Solving -77 + 18u + 3u2 = 0 Solving for variable 'u'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -25.66666667 + 6u + u2 = 0 Move the constant term to the right: Add '25.66666667' to each side of the equation. -25.66666667 + 6u + 25.66666667 + u2 = 0 + 25.66666667 Reorder the terms: -25.66666667 + 25.66666667 + 6u + u2 = 0 + 25.66666667 Combine like terms: -25.66666667 + 25.66666667 = 0.00000000 0.00000000 + 6u + u2 = 0 + 25.66666667 6u + u2 = 0 + 25.66666667 Combine like terms: 0 + 25.66666667 = 25.66666667 6u + u2 = 25.66666667 The u term is 6u. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6u + 9 + u2 = 25.66666667 + 9 Reorder the terms: 9 + 6u + u2 = 25.66666667 + 9 Combine like terms: 25.66666667 + 9 = 34.66666667 9 + 6u + u2 = 34.66666667 Factor a perfect square on the left side: (u + 3)(u + 3) = 34.66666667 Calculate the square root of the right side: 5.887840578 Break this problem into two subproblems by setting (u + 3) equal to 5.887840578 and -5.887840578.Subproblem 1
u + 3 = 5.887840578 Simplifying u + 3 = 5.887840578 Reorder the terms: 3 + u = 5.887840578 Solving 3 + u = 5.887840578 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = 5.887840578 + -3 Combine like terms: 3 + -3 = 0 0 + u = 5.887840578 + -3 u = 5.887840578 + -3 Combine like terms: 5.887840578 + -3 = 2.887840578 u = 2.887840578 Simplifying u = 2.887840578Subproblem 2
u + 3 = -5.887840578 Simplifying u + 3 = -5.887840578 Reorder the terms: 3 + u = -5.887840578 Solving 3 + u = -5.887840578 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + u = -5.887840578 + -3 Combine like terms: 3 + -3 = 0 0 + u = -5.887840578 + -3 u = -5.887840578 + -3 Combine like terms: -5.887840578 + -3 = -8.887840578 u = -8.887840578 Simplifying u = -8.887840578Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.887840578, -8.887840578}
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