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Simplifying (-3u2 + u) + (-5u2 + -7u + 4) = 0 Reorder the terms: (u + -3u2) + (-5u2 + -7u + 4) = 0 Remove parenthesis around (u + -3u2) u + -3u2 + (-5u2 + -7u + 4) = 0 Reorder the terms: u + -3u2 + (4 + -7u + -5u2) = 0 Remove parenthesis around (4 + -7u + -5u2) u + -3u2 + 4 + -7u + -5u2 = 0 Reorder the terms: 4 + u + -7u + -3u2 + -5u2 = 0 Combine like terms: u + -7u = -6u 4 + -6u + -3u2 + -5u2 = 0 Combine like terms: -3u2 + -5u2 = -8u2 4 + -6u + -8u2 = 0 Solving 4 + -6u + -8u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3u + -4u2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3u + -4u2)' equal to zero and attempt to solve: Simplifying 2 + -3u + -4u2 = 0 Solving 2 + -3u + -4u2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 0.75u + u2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.75u + 0.5 + u2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.75u + u2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.75u + u2 = 0 + 0.5 0.75u + u2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.75u + u2 = 0.5 The u term is 0.75u. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75u + 0.140625 + u2 = 0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75u + u2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + 0.75u + u2 = 0.640625 Factor a perfect square on the left side: (u + 0.375)(u + 0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (u + 0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
u + 0.375 = 0.80039053 Simplifying u + 0.375 = 0.80039053 Reorder the terms: 0.375 + u = 0.80039053 Solving 0.375 + u = 0.80039053 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + u = 0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + u = 0.80039053 + -0.375 u = 0.80039053 + -0.375 Combine like terms: 0.80039053 + -0.375 = 0.42539053 u = 0.42539053 Simplifying u = 0.42539053Subproblem 2
u + 0.375 = -0.80039053 Simplifying u + 0.375 = -0.80039053 Reorder the terms: 0.375 + u = -0.80039053 Solving 0.375 + u = -0.80039053 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + u = -0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + u = -0.80039053 + -0.375 u = -0.80039053 + -0.375 Combine like terms: -0.80039053 + -0.375 = -1.17539053 u = -1.17539053 Simplifying u = -1.17539053Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.42539053, -1.17539053}Solution
u = {0.42539053, -1.17539053}
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