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Simplifying (u + 4)(u + 4) = 2u2 + -10u + 8 Reorder the terms: (4 + u)(u + 4) = 2u2 + -10u + 8 Reorder the terms: (4 + u)(4 + u) = 2u2 + -10u + 8 Multiply (4 + u) * (4 + u) (4(4 + u) + u(4 + u)) = 2u2 + -10u + 8 ((4 * 4 + u * 4) + u(4 + u)) = 2u2 + -10u + 8 ((16 + 4u) + u(4 + u)) = 2u2 + -10u + 8 (16 + 4u + (4 * u + u * u)) = 2u2 + -10u + 8 (16 + 4u + (4u + u2)) = 2u2 + -10u + 8 Combine like terms: 4u + 4u = 8u (16 + 8u + u2) = 2u2 + -10u + 8 Reorder the terms: 16 + 8u + u2 = 8 + -10u + 2u2 Solving 16 + 8u + u2 = 8 + -10u + 2u2 Solving for variable 'u'. Reorder the terms: 16 + -8 + 8u + 10u + u2 + -2u2 = 8 + -10u + 2u2 + -8 + 10u + -2u2 Combine like terms: 16 + -8 = 8 8 + 8u + 10u + u2 + -2u2 = 8 + -10u + 2u2 + -8 + 10u + -2u2 Combine like terms: 8u + 10u = 18u 8 + 18u + u2 + -2u2 = 8 + -10u + 2u2 + -8 + 10u + -2u2 Combine like terms: u2 + -2u2 = -1u2 8 + 18u + -1u2 = 8 + -10u + 2u2 + -8 + 10u + -2u2 Reorder the terms: 8 + 18u + -1u2 = 8 + -8 + -10u + 10u + 2u2 + -2u2 Combine like terms: 8 + -8 = 0 8 + 18u + -1u2 = 0 + -10u + 10u + 2u2 + -2u2 8 + 18u + -1u2 = -10u + 10u + 2u2 + -2u2 Combine like terms: -10u + 10u = 0 8 + 18u + -1u2 = 0 + 2u2 + -2u2 8 + 18u + -1u2 = 2u2 + -2u2 Combine like terms: 2u2 + -2u2 = 0 8 + 18u + -1u2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -18u + u2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -18u + 8 + u2 = 0 + 8 Reorder the terms: -8 + 8 + -18u + u2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -18u + u2 = 0 + 8 -18u + u2 = 0 + 8 Combine like terms: 0 + 8 = 8 -18u + u2 = 8 The u term is -18u. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18u + 81 + u2 = 8 + 81 Reorder the terms: 81 + -18u + u2 = 8 + 81 Combine like terms: 8 + 81 = 89 81 + -18u + u2 = 89 Factor a perfect square on the left side: (u + -9)(u + -9) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (u + -9) equal to 9.433981132 and -9.433981132.Subproblem 1
u + -9 = 9.433981132 Simplifying u + -9 = 9.433981132 Reorder the terms: -9 + u = 9.433981132 Solving -9 + u = 9.433981132 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = 9.433981132 + 9 Combine like terms: -9 + 9 = 0 0 + u = 9.433981132 + 9 u = 9.433981132 + 9 Combine like terms: 9.433981132 + 9 = 18.433981132 u = 18.433981132 Simplifying u = 18.433981132Subproblem 2
u + -9 = -9.433981132 Simplifying u + -9 = -9.433981132 Reorder the terms: -9 + u = -9.433981132 Solving -9 + u = -9.433981132 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + u = -9.433981132 + 9 Combine like terms: -9 + 9 = 0 0 + u = -9.433981132 + 9 u = -9.433981132 + 9 Combine like terms: -9.433981132 + 9 = -0.433981132 u = -0.433981132 Simplifying u = -0.433981132Solution
The solution to the problem is based on the solutions from the subproblems. u = {18.433981132, -0.433981132}
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