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Simplifying u2 + 7u + -2 = 0 Reorder the terms: -2 + 7u + u2 = 0 Solving -2 + 7u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 7u + 2 + u2 = 0 + 2 Reorder the terms: -2 + 2 + 7u + u2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 7u + u2 = 0 + 2 7u + u2 = 0 + 2 Combine like terms: 0 + 2 = 2 7u + u2 = 2 The u term is 7u. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7u + 12.25 + u2 = 2 + 12.25 Reorder the terms: 12.25 + 7u + u2 = 2 + 12.25 Combine like terms: 2 + 12.25 = 14.25 12.25 + 7u + u2 = 14.25 Factor a perfect square on the left side: (u + 3.5)(u + 3.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (u + 3.5) equal to 3.774917218 and -3.774917218.Subproblem 1
u + 3.5 = 3.774917218 Simplifying u + 3.5 = 3.774917218 Reorder the terms: 3.5 + u = 3.774917218 Solving 3.5 + u = 3.774917218 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + u = 3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = 3.774917218 + -3.5 u = 3.774917218 + -3.5 Combine like terms: 3.774917218 + -3.5 = 0.274917218 u = 0.274917218 Simplifying u = 0.274917218Subproblem 2
u + 3.5 = -3.774917218 Simplifying u + 3.5 = -3.774917218 Reorder the terms: 3.5 + u = -3.774917218 Solving 3.5 + u = -3.774917218 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + u = -3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + u = -3.774917218 + -3.5 u = -3.774917218 + -3.5 Combine like terms: -3.774917218 + -3.5 = -7.274917218 u = -7.274917218 Simplifying u = -7.274917218Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.274917218, -7.274917218}
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