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Simplifying u2 + 4u + -15 = 0 Reorder the terms: -15 + 4u + u2 = 0 Solving -15 + 4u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 4u + 15 + u2 = 0 + 15 Reorder the terms: -15 + 15 + 4u + u2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 4u + u2 = 0 + 15 4u + u2 = 0 + 15 Combine like terms: 0 + 15 = 15 4u + u2 = 15 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 = 15 + 4 Reorder the terms: 4 + 4u + u2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + 4u + u2 = 19 Factor a perfect square on the left side: (u + 2)(u + 2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (u + 2) equal to 4.358898944 and -4.358898944.Subproblem 1
u + 2 = 4.358898944 Simplifying u + 2 = 4.358898944 Reorder the terms: 2 + u = 4.358898944 Solving 2 + u = 4.358898944 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 = 4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + u = 4.358898944 + -2 u = 4.358898944 + -2 Combine like terms: 4.358898944 + -2 = 2.358898944 u = 2.358898944 Simplifying u = 2.358898944Subproblem 2
u + 2 = -4.358898944 Simplifying u + 2 = -4.358898944 Reorder the terms: 2 + u = -4.358898944 Solving 2 + u = -4.358898944 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 = -4.358898944 + -2 Combine like terms: 2 + -2 = 0 0 + u = -4.358898944 + -2 u = -4.358898944 + -2 Combine like terms: -4.358898944 + -2 = -6.358898944 u = -6.358898944 Simplifying u = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. u = {2.358898944, -6.358898944}
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