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Simplifying u2 + -13u + 28 = 0 Reorder the terms: 28 + -13u + u2 = 0 Solving 28 + -13u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -13u + -28 + u2 = 0 + -28 Reorder the terms: 28 + -28 + -13u + u2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -13u + u2 = 0 + -28 -13u + u2 = 0 + -28 Combine like terms: 0 + -28 = -28 -13u + u2 = -28 The u term is -13u. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13u + 42.25 + u2 = -28 + 42.25 Reorder the terms: 42.25 + -13u + u2 = -28 + 42.25 Combine like terms: -28 + 42.25 = 14.25 42.25 + -13u + u2 = 14.25 Factor a perfect square on the left side: (u + -6.5)(u + -6.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (u + -6.5) equal to 3.774917218 and -3.774917218.Subproblem 1
u + -6.5 = 3.774917218 Simplifying u + -6.5 = 3.774917218 Reorder the terms: -6.5 + u = 3.774917218 Solving -6.5 + u = 3.774917218 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = 3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = 3.774917218 + 6.5 u = 3.774917218 + 6.5 Combine like terms: 3.774917218 + 6.5 = 10.274917218 u = 10.274917218 Simplifying u = 10.274917218Subproblem 2
u + -6.5 = -3.774917218 Simplifying u + -6.5 = -3.774917218 Reorder the terms: -6.5 + u = -3.774917218 Solving -6.5 + u = -3.774917218 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u = -3.774917218 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u = -3.774917218 + 6.5 u = -3.774917218 + 6.5 Combine like terms: -3.774917218 + 6.5 = 2.725082782 u = 2.725082782 Simplifying u = 2.725082782Solution
The solution to the problem is based on the solutions from the subproblems. u = {10.274917218, 2.725082782}
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