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Simplifying (-3u2 + -9u + -5) + -1(u2 + 7u + -5) + (-5u2 + -7u + -1) = 0 Reorder the terms: (-5 + -9u + -3u2) + -1(u2 + 7u + -5) + (-5u2 + -7u + -1) = 0 Remove parenthesis around (-5 + -9u + -3u2) -5 + -9u + -3u2 + -1(u2 + 7u + -5) + (-5u2 + -7u + -1) = 0 Reorder the terms: -5 + -9u + -3u2 + -1(-5 + 7u + u2) + (-5u2 + -7u + -1) = 0 -5 + -9u + -3u2 + (-5 * -1 + 7u * -1 + u2 * -1) + (-5u2 + -7u + -1) = 0 -5 + -9u + -3u2 + (5 + -7u + -1u2) + (-5u2 + -7u + -1) = 0 Reorder the terms: -5 + -9u + -3u2 + 5 + -7u + -1u2 + (-1 + -7u + -5u2) = 0 Remove parenthesis around (-1 + -7u + -5u2) -5 + -9u + -3u2 + 5 + -7u + -1u2 + -1 + -7u + -5u2 = 0 Reorder the terms: -5 + 5 + -1 + -9u + -7u + -7u + -3u2 + -1u2 + -5u2 = 0 Combine like terms: -5 + 5 = 0 0 + -1 + -9u + -7u + -7u + -3u2 + -1u2 + -5u2 = 0 -1 + -9u + -7u + -7u + -3u2 + -1u2 + -5u2 = 0 Combine like terms: -9u + -7u = -16u -1 + -16u + -7u + -3u2 + -1u2 + -5u2 = 0 Combine like terms: -16u + -7u = -23u -1 + -23u + -3u2 + -1u2 + -5u2 = 0 Combine like terms: -3u2 + -1u2 = -4u2 -1 + -23u + -4u2 + -5u2 = 0 Combine like terms: -4u2 + -5u2 = -9u2 -1 + -23u + -9u2 = 0 Solving -1 + -23u + -9u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 23u + 9u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 23u + 9u2)' equal to zero and attempt to solve: Simplifying 1 + 23u + 9u2 = 0 Solving 1 + 23u + 9u2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 2.555555556u + u2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 2.555555556u + -0.1111111111 + u2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 2.555555556u + u2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 2.555555556u + u2 = 0 + -0.1111111111 2.555555556u + u2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 2.555555556u + u2 = -0.1111111111 The u term is 2.555555556u. Take half its coefficient (1.277777778). Square it (1.632716050) and add it to both sides. Add '1.632716050' to each side of the equation. 2.555555556u + 1.632716050 + u2 = -0.1111111111 + 1.632716050 Reorder the terms: 1.632716050 + 2.555555556u + u2 = -0.1111111111 + 1.632716050 Combine like terms: -0.1111111111 + 1.632716050 = 1.5216049389 1.632716050 + 2.555555556u + u2 = 1.5216049389 Factor a perfect square on the left side: (u + 1.277777778)(u + 1.277777778) = 1.5216049389 Calculate the square root of the right side: 1.233533518 Break this problem into two subproblems by setting (u + 1.277777778) equal to 1.233533518 and -1.233533518.Subproblem 1
u + 1.277777778 = 1.233533518 Simplifying u + 1.277777778 = 1.233533518 Reorder the terms: 1.277777778 + u = 1.233533518 Solving 1.277777778 + u = 1.233533518 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + u = 1.233533518 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + u = 1.233533518 + -1.277777778 u = 1.233533518 + -1.277777778 Combine like terms: 1.233533518 + -1.277777778 = -0.04424426 u = -0.04424426 Simplifying u = -0.04424426Subproblem 2
u + 1.277777778 = -1.233533518 Simplifying u + 1.277777778 = -1.233533518 Reorder the terms: 1.277777778 + u = -1.233533518 Solving 1.277777778 + u = -1.233533518 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.277777778' to each side of the equation. 1.277777778 + -1.277777778 + u = -1.233533518 + -1.277777778 Combine like terms: 1.277777778 + -1.277777778 = 0.000000000 0.000000000 + u = -1.233533518 + -1.277777778 u = -1.233533518 + -1.277777778 Combine like terms: -1.233533518 + -1.277777778 = -2.511311296 u = -2.511311296 Simplifying u = -2.511311296Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.04424426, -2.511311296}Solution
u = {-0.04424426, -2.511311296}
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