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Simplifying (u + -4)(u + -4) + -20 = 0 Reorder the terms: (-4 + u)(u + -4) + -20 = 0 Reorder the terms: (-4 + u)(-4 + u) + -20 = 0 Multiply (-4 + u) * (-4 + u) (-4(-4 + u) + u(-4 + u)) + -20 = 0 ((-4 * -4 + u * -4) + u(-4 + u)) + -20 = 0 ((16 + -4u) + u(-4 + u)) + -20 = 0 (16 + -4u + (-4 * u + u * u)) + -20 = 0 (16 + -4u + (-4u + u2)) + -20 = 0 Combine like terms: -4u + -4u = -8u (16 + -8u + u2) + -20 = 0 Reorder the terms: 16 + -20 + -8u + u2 = 0 Combine like terms: 16 + -20 = -4 -4 + -8u + u2 = 0 Solving -4 + -8u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -8u + 4 + u2 = 0 + 4 Reorder the terms: -4 + 4 + -8u + u2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -8u + u2 = 0 + 4 -8u + u2 = 0 + 4 Combine like terms: 0 + 4 = 4 -8u + u2 = 4 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 = 4 + 16 Reorder the terms: 16 + -8u + u2 = 4 + 16 Combine like terms: 4 + 16 = 20 16 + -8u + u2 = 20 Factor a perfect square on the left side: (u + -4)(u + -4) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (u + -4) equal to 4.472135955 and -4.472135955.Subproblem 1
u + -4 = 4.472135955 Simplifying u + -4 = 4.472135955 Reorder the terms: -4 + u = 4.472135955 Solving -4 + u = 4.472135955 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 = 4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + u = 4.472135955 + 4 u = 4.472135955 + 4 Combine like terms: 4.472135955 + 4 = 8.472135955 u = 8.472135955 Simplifying u = 8.472135955Subproblem 2
u + -4 = -4.472135955 Simplifying u + -4 = -4.472135955 Reorder the terms: -4 + u = -4.472135955 Solving -4 + u = -4.472135955 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 = -4.472135955 + 4 Combine like terms: -4 + 4 = 0 0 + u = -4.472135955 + 4 u = -4.472135955 + 4 Combine like terms: -4.472135955 + 4 = -0.472135955 u = -0.472135955 Simplifying u = -0.472135955Solution
The solution to the problem is based on the solutions from the subproblems. u = {8.472135955, -0.472135955}
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