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Simplifying u2 + 8u = 19 Reorder the terms: 8u + u2 = 19 Solving 8u + u2 = 19 Solving for variable 'u'. Reorder the terms: -19 + 8u + u2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + 8u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 8u + 19 + u2 = 0 + 19 Reorder the terms: -19 + 19 + 8u + u2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 8u + u2 = 0 + 19 8u + u2 = 0 + 19 Combine like terms: 0 + 19 = 19 8u + u2 = 19 The u term is 8u. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8u + 16 + u2 = 19 + 16 Reorder the terms: 16 + 8u + u2 = 19 + 16 Combine like terms: 19 + 16 = 35 16 + 8u + u2 = 35 Factor a perfect square on the left side: (u + 4)(u + 4) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (u + 4) equal to 5.916079783 and -5.916079783.Subproblem 1
u + 4 = 5.916079783 Simplifying u + 4 = 5.916079783 Reorder the terms: 4 + u = 5.916079783 Solving 4 + u = 5.916079783 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = 5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + u = 5.916079783 + -4 u = 5.916079783 + -4 Combine like terms: 5.916079783 + -4 = 1.916079783 u = 1.916079783 Simplifying u = 1.916079783Subproblem 2
u + 4 = -5.916079783 Simplifying u + 4 = -5.916079783 Reorder the terms: 4 + u = -5.916079783 Solving 4 + u = -5.916079783 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + u = -5.916079783 + -4 Combine like terms: 4 + -4 = 0 0 + u = -5.916079783 + -4 u = -5.916079783 + -4 Combine like terms: -5.916079783 + -4 = -9.916079783 u = -9.916079783 Simplifying u = -9.916079783Solution
The solution to the problem is based on the solutions from the subproblems. u = {1.916079783, -9.916079783}
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