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Simplifying 3u2 = 18u + -9 Reorder the terms: 3u2 = -9 + 18u Solving 3u2 = -9 + 18u Solving for variable 'u'. Reorder the terms: 9 + -18u + 3u2 = -9 + 18u + 9 + -18u Reorder the terms: 9 + -18u + 3u2 = -9 + 9 + 18u + -18u Combine like terms: -9 + 9 = 0 9 + -18u + 3u2 = 0 + 18u + -18u 9 + -18u + 3u2 = 18u + -18u Combine like terms: 18u + -18u = 0 9 + -18u + 3u2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -6u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -6u + u2)' equal to zero and attempt to solve: Simplifying 3 + -6u + u2 = 0 Solving 3 + -6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6u + -3 + u2 = 0 + -3 Reorder the terms: 3 + -3 + -6u + u2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6u + u2 = 0 + -3 -6u + u2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6u + u2 = -3 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 = -3 + 9 Reorder the terms: 9 + -6u + u2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6u + u2 = 6 Factor a perfect square on the left side: (u + -3)(u + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (u + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
u + -3 = 2.449489743 Simplifying u + -3 = 2.449489743 Reorder the terms: -3 + u = 2.449489743 Solving -3 + u = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + u = 2.449489743 + 3 u = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 u = 5.449489743 Simplifying u = 5.449489743Subproblem 2
u + -3 = -2.449489743 Simplifying u + -3 = -2.449489743 Reorder the terms: -3 + u = -2.449489743 Solving -3 + u = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + u = -2.449489743 + 3 u = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 u = 0.550510257 Simplifying u = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. u = {5.449489743, 0.550510257}Solution
u = {5.449489743, 0.550510257}
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