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Simplifying (-2u2 + -8u + -4) + -1(9u2 + 5u + -7) + (-9u2 + -6u + -7) = 0 Reorder the terms: (-4 + -8u + -2u2) + -1(9u2 + 5u + -7) + (-9u2 + -6u + -7) = 0 Remove parenthesis around (-4 + -8u + -2u2) -4 + -8u + -2u2 + -1(9u2 + 5u + -7) + (-9u2 + -6u + -7) = 0 Reorder the terms: -4 + -8u + -2u2 + -1(-7 + 5u + 9u2) + (-9u2 + -6u + -7) = 0 -4 + -8u + -2u2 + (-7 * -1 + 5u * -1 + 9u2 * -1) + (-9u2 + -6u + -7) = 0 -4 + -8u + -2u2 + (7 + -5u + -9u2) + (-9u2 + -6u + -7) = 0 Reorder the terms: -4 + -8u + -2u2 + 7 + -5u + -9u2 + (-7 + -6u + -9u2) = 0 Remove parenthesis around (-7 + -6u + -9u2) -4 + -8u + -2u2 + 7 + -5u + -9u2 + -7 + -6u + -9u2 = 0 Reorder the terms: -4 + 7 + -7 + -8u + -5u + -6u + -2u2 + -9u2 + -9u2 = 0 Combine like terms: -4 + 7 = 3 3 + -7 + -8u + -5u + -6u + -2u2 + -9u2 + -9u2 = 0 Combine like terms: 3 + -7 = -4 -4 + -8u + -5u + -6u + -2u2 + -9u2 + -9u2 = 0 Combine like terms: -8u + -5u = -13u -4 + -13u + -6u + -2u2 + -9u2 + -9u2 = 0 Combine like terms: -13u + -6u = -19u -4 + -19u + -2u2 + -9u2 + -9u2 = 0 Combine like terms: -2u2 + -9u2 = -11u2 -4 + -19u + -11u2 + -9u2 = 0 Combine like terms: -11u2 + -9u2 = -20u2 -4 + -19u + -20u2 = 0 Solving -4 + -19u + -20u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 19u + 20u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 19u + 20u2)' equal to zero and attempt to solve: Simplifying 4 + 19u + 20u2 = 0 Solving 4 + 19u + 20u2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.2 + 0.95u + u2 = 0.0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.95u + -0.2 + u2 = 0.0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.95u + u2 = 0.0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.95u + u2 = 0.0 + -0.2 0.95u + u2 = 0.0 + -0.2 Combine like terms: 0.0 + -0.2 = -0.2 0.95u + u2 = -0.2 The u term is 0.95u. Take half its coefficient (0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. 0.95u + 0.225625 + u2 = -0.2 + 0.225625 Reorder the terms: 0.225625 + 0.95u + u2 = -0.2 + 0.225625 Combine like terms: -0.2 + 0.225625 = 0.025625 0.225625 + 0.95u + u2 = 0.025625 Factor a perfect square on the left side: (u + 0.475)(u + 0.475) = 0.025625 Calculate the square root of the right side: 0.160078106 Break this problem into two subproblems by setting (u + 0.475) equal to 0.160078106 and -0.160078106.Subproblem 1
u + 0.475 = 0.160078106 Simplifying u + 0.475 = 0.160078106 Reorder the terms: 0.475 + u = 0.160078106 Solving 0.475 + u = 0.160078106 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + u = 0.160078106 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + u = 0.160078106 + -0.475 u = 0.160078106 + -0.475 Combine like terms: 0.160078106 + -0.475 = -0.314921894 u = -0.314921894 Simplifying u = -0.314921894Subproblem 2
u + 0.475 = -0.160078106 Simplifying u + 0.475 = -0.160078106 Reorder the terms: 0.475 + u = -0.160078106 Solving 0.475 + u = -0.160078106 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + u = -0.160078106 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + u = -0.160078106 + -0.475 u = -0.160078106 + -0.475 Combine like terms: -0.160078106 + -0.475 = -0.635078106 u = -0.635078106 Simplifying u = -0.635078106Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.314921894, -0.635078106}Solution
u = {-0.314921894, -0.635078106}
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