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Simplifying u2 + -4u = 25 Reorder the terms: -4u + u2 = 25 Solving -4u + u2 = 25 Solving for variable 'u'. Reorder the terms: -25 + -4u + u2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -4u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -4u + 25 + u2 = 0 + 25 Reorder the terms: -25 + 25 + -4u + u2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4u + u2 = 0 + 25 -4u + u2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4u + u2 = 25 The u term is -4u. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4u + 4 + u2 = 25 + 4 Reorder the terms: 4 + -4u + u2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4u + u2 = 29 Factor a perfect square on the left side: (u + -2)(u + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (u + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
u + -2 = 5.385164807 Simplifying u + -2 = 5.385164807 Reorder the terms: -2 + u = 5.385164807 Solving -2 + u = 5.385164807 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + u = 5.385164807 + 2 u = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 u = 7.385164807 Simplifying u = 7.385164807Subproblem 2
u + -2 = -5.385164807 Simplifying u + -2 = -5.385164807 Reorder the terms: -2 + u = -5.385164807 Solving -2 + u = -5.385164807 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + u = -5.385164807 + 2 u = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 u = -3.385164807 Simplifying u = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.385164807, -3.385164807}
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