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Simplifying -1u2 + -6u + -7 = 0 Reorder the terms: -7 + -6u + -1u2 = 0 Solving -7 + -6u + -1u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 6u + u2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 6u + u2)' equal to zero and attempt to solve: Simplifying 7 + 6u + u2 = 0 Solving 7 + 6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6u + -7 + u2 = 0 + -7 Reorder the terms: 7 + -7 + 6u + u2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6u + u2 = 0 + -7 6u + u2 = 0 + -7 Combine like terms: 0 + -7 = -7 6u + u2 = -7 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 = -7 + 9 Reorder the terms: 9 + 6u + u2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + 6u + u2 = 2 Factor a perfect square on the left side: (u + 3)(u + 3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (u + 3) equal to 1.414213562 and -1.414213562.Subproblem 1
u + 3 = 1.414213562 Simplifying u + 3 = 1.414213562 Reorder the terms: 3 + u = 1.414213562 Solving 3 + u = 1.414213562 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 = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + u = 1.414213562 + -3 u = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 u = -1.585786438 Simplifying u = -1.585786438Subproblem 2
u + 3 = -1.414213562 Simplifying u + 3 = -1.414213562 Reorder the terms: 3 + u = -1.414213562 Solving 3 + u = -1.414213562 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 = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + u = -1.414213562 + -3 u = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 u = -4.414213562 Simplifying u = -4.414213562Solution
The solution to the problem is based on the solutions from the subproblems. u = {-1.585786438, -4.414213562}Solution
u = {-1.585786438, -4.414213562}
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