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Simplifying ((u + 8)(u + 8)) + -24 = 0 Reorder the terms: ((8 + u)(u + 8)) + -24 = 0 Reorder the terms: ((8 + u)(8 + u)) + -24 = 0 Multiply (8 + u) * (8 + u) ((8(8 + u) + u(8 + u))) + -24 = 0 (((8 * 8 + u * 8) + u(8 + u))) + -24 = 0 (((64 + 8u) + u(8 + u))) + -24 = 0 ((64 + 8u + (8 * u + u * u))) + -24 = 0 ((64 + 8u + (8u + u2))) + -24 = 0 Combine like terms: 8u + 8u = 16u ((64 + 16u + u2)) + -24 = 0 (64 + 16u + u2) + -24 = 0 Remove parenthesis around (64 + 16u + u2) 64 + 16u + u2 + -24 = 0 Reorder the terms: 64 + -24 + 16u + u2 = 0 Combine like terms: 64 + -24 = 40 40 + 16u + u2 = 0 Solving 40 + 16u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 16u + -40 + u2 = 0 + -40 Reorder the terms: 40 + -40 + 16u + u2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 16u + u2 = 0 + -40 16u + u2 = 0 + -40 Combine like terms: 0 + -40 = -40 16u + u2 = -40 The u term is 16u. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16u + 64 + u2 = -40 + 64 Reorder the terms: 64 + 16u + u2 = -40 + 64 Combine like terms: -40 + 64 = 24 64 + 16u + u2 = 24 Factor a perfect square on the left side: (u + 8)(u + 8) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (u + 8) equal to 4.898979486 and -4.898979486.Subproblem 1
u + 8 = 4.898979486 Simplifying u + 8 = 4.898979486 Reorder the terms: 8 + u = 4.898979486 Solving 8 + u = 4.898979486 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = 4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + u = 4.898979486 + -8 u = 4.898979486 + -8 Combine like terms: 4.898979486 + -8 = -3.101020514 u = -3.101020514 Simplifying u = -3.101020514Subproblem 2
u + 8 = -4.898979486 Simplifying u + 8 = -4.898979486 Reorder the terms: 8 + u = -4.898979486 Solving 8 + u = -4.898979486 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + u = -4.898979486 + -8 Combine like terms: 8 + -8 = 0 0 + u = -4.898979486 + -8 u = -4.898979486 + -8 Combine like terms: -4.898979486 + -8 = -12.898979486 u = -12.898979486 Simplifying u = -12.898979486Solution
The solution to the problem is based on the solutions from the subproblems. u = {-3.101020514, -12.898979486}
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