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Simplifying u2 + -2u = 4u + 8 Reorder the terms: -2u + u2 = 4u + 8 Reorder the terms: -2u + u2 = 8 + 4u Solving -2u + u2 = 8 + 4u Solving for variable 'u'. Reorder the terms: -8 + -2u + -4u + u2 = 8 + 4u + -8 + -4u Combine like terms: -2u + -4u = -6u -8 + -6u + u2 = 8 + 4u + -8 + -4u Reorder the terms: -8 + -6u + u2 = 8 + -8 + 4u + -4u Combine like terms: 8 + -8 = 0 -8 + -6u + u2 = 0 + 4u + -4u -8 + -6u + u2 = 4u + -4u Combine like terms: 4u + -4u = 0 -8 + -6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -6u + 8 + u2 = 0 + 8 Reorder the terms: -8 + 8 + -6u + u2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -6u + u2 = 0 + 8 -6u + u2 = 0 + 8 Combine like terms: 0 + 8 = 8 -6u + u2 = 8 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = 8 + 9 Reorder the terms: 9 + -6u + u2 = 8 + 9 Combine like terms: 8 + 9 = 17 9 + -6u + u2 = 17 Factor a perfect square on the left side: (u + -3)(u + -3) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (u + -3) equal to 4.123105626 and -4.123105626.Subproblem 1
u + -3 = 4.123105626 Simplifying u + -3 = 4.123105626 Reorder the terms: -3 + u = 4.123105626 Solving -3 + u = 4.123105626 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + u = 4.123105626 + 3 u = 4.123105626 + 3 Combine like terms: 4.123105626 + 3 = 7.123105626 u = 7.123105626 Simplifying u = 7.123105626Subproblem 2
u + -3 = -4.123105626 Simplifying u + -3 = -4.123105626 Reorder the terms: -3 + u = -4.123105626 Solving -3 + u = -4.123105626 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -4.123105626 + 3 Combine like terms: -3 + 3 = 0 0 + u = -4.123105626 + 3 u = -4.123105626 + 3 Combine like terms: -4.123105626 + 3 = -1.123105626 u = -1.123105626 Simplifying u = -1.123105626Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.123105626, -1.123105626}
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