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Simplifying 0 = u2 + 8u + -8 Reorder the terms: 0 = -8 + 8u + u2 Solving 0 = -8 + 8u + u2 Solving for variable 'u'. Combine like terms: 0 + 8 = 8 8 + -8u + -1u2 = -8 + 8u + u2 + 8 + -8u + -1u2 Reorder the terms: 8 + -8u + -1u2 = -8 + 8 + 8u + -8u + u2 + -1u2 Combine like terms: -8 + 8 = 0 8 + -8u + -1u2 = 0 + 8u + -8u + u2 + -1u2 8 + -8u + -1u2 = 8u + -8u + u2 + -1u2 Combine like terms: 8u + -8u = 0 8 + -8u + -1u2 = 0 + u2 + -1u2 8 + -8u + -1u2 = u2 + -1u2 Combine like terms: u2 + -1u2 = 0 8 + -8u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + 8u + u2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 8u + 8 + u2 = 0 + 8 Reorder the terms: -8 + 8 + 8u + u2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 8u + u2 = 0 + 8 8u + u2 = 0 + 8 Combine like terms: 0 + 8 = 8 8u + u2 = 8 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 = 8 + 16 Reorder the terms: 16 + 8u + u2 = 8 + 16 Combine like terms: 8 + 16 = 24 16 + 8u + u2 = 24 Factor a perfect square on the left side: (u + 4)(u + 4) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (u + 4) equal to 4.898979486 and -4.898979486.Subproblem 1
u + 4 = 4.898979486 Simplifying u + 4 = 4.898979486 Reorder the terms: 4 + u = 4.898979486 Solving 4 + u = 4.898979486 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 = 4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + u = 4.898979486 + -4 u = 4.898979486 + -4 Combine like terms: 4.898979486 + -4 = 0.898979486 u = 0.898979486 Simplifying u = 0.898979486Subproblem 2
u + 4 = -4.898979486 Simplifying u + 4 = -4.898979486 Reorder the terms: 4 + u = -4.898979486 Solving 4 + u = -4.898979486 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 = -4.898979486 + -4 Combine like terms: 4 + -4 = 0 0 + u = -4.898979486 + -4 u = -4.898979486 + -4 Combine like terms: -4.898979486 + -4 = -8.898979486 u = -8.898979486 Simplifying u = -8.898979486Solution
The solution to the problem is based on the solutions from the subproblems. u = {0.898979486, -8.898979486}
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