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Simplifying u2 + -15u + 38 = 0 Reorder the terms: 38 + -15u + u2 = 0 Solving 38 + -15u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -15u + -38 + u2 = 0 + -38 Reorder the terms: 38 + -38 + -15u + u2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -15u + u2 = 0 + -38 -15u + u2 = 0 + -38 Combine like terms: 0 + -38 = -38 -15u + u2 = -38 The u term is -15u. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15u + 56.25 + u2 = -38 + 56.25 Reorder the terms: 56.25 + -15u + u2 = -38 + 56.25 Combine like terms: -38 + 56.25 = 18.25 56.25 + -15u + u2 = 18.25 Factor a perfect square on the left side: (u + -7.5)(u + -7.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (u + -7.5) equal to 4.272001873 and -4.272001873.Subproblem 1
u + -7.5 = 4.272001873 Simplifying u + -7.5 = 4.272001873 Reorder the terms: -7.5 + u = 4.272001873 Solving -7.5 + u = 4.272001873 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u = 4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u = 4.272001873 + 7.5 u = 4.272001873 + 7.5 Combine like terms: 4.272001873 + 7.5 = 11.772001873 u = 11.772001873 Simplifying u = 11.772001873Subproblem 2
u + -7.5 = -4.272001873 Simplifying u + -7.5 = -4.272001873 Reorder the terms: -7.5 + u = -4.272001873 Solving -7.5 + u = -4.272001873 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + u = -4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + u = -4.272001873 + 7.5 u = -4.272001873 + 7.5 Combine like terms: -4.272001873 + 7.5 = 3.227998127 u = 3.227998127 Simplifying u = 3.227998127Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.772001873, 3.227998127}
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