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Simplifying u2 + -8u + -7 = 0 Reorder the terms: -7 + -8u + u2 = 0 Solving -7 + -8u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -8u + 7 + u2 = 0 + 7 Reorder the terms: -7 + 7 + -8u + u2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8u + u2 = 0 + 7 -8u + u2 = 0 + 7 Combine like terms: 0 + 7 = 7 -8u + u2 = 7 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 = 7 + 16 Reorder the terms: 16 + -8u + u2 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8u + u2 = 23 Factor a perfect square on the left side: (u + -4)(u + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (u + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
u + -4 = 4.795831523 Simplifying u + -4 = 4.795831523 Reorder the terms: -4 + u = 4.795831523 Solving -4 + u = 4.795831523 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 = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + u = 4.795831523 + 4 u = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 u = 8.795831523 Simplifying u = 8.795831523Subproblem 2
u + -4 = -4.795831523 Simplifying u + -4 = -4.795831523 Reorder the terms: -4 + u = -4.795831523 Solving -4 + u = -4.795831523 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 = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + u = -4.795831523 + 4 u = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 u = -0.795831523 Simplifying u = -0.795831523Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.795831523, -0.795831523}
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