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Simplifying u2 + 10u + 24 * 8u + 32 = 0 Multiply 24 * 8 u2 + 10u + 192u + 32 = 0 Reorder the terms: 32 + 10u + 192u + u2 = 0 Combine like terms: 10u + 192u = 202u 32 + 202u + u2 = 0 Solving 32 + 202u + u2 = 0 Solving for variable 'u'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 202u + -32 + u2 = 0 + -32 Reorder the terms: 32 + -32 + 202u + u2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 202u + u2 = 0 + -32 202u + u2 = 0 + -32 Combine like terms: 0 + -32 = -32 202u + u2 = -32 The u term is 202u. Take half its coefficient (101). Square it (10201) and add it to both sides. Add '10201' to each side of the equation. 202u + 10201 + u2 = -32 + 10201 Reorder the terms: 10201 + 202u + u2 = -32 + 10201 Combine like terms: -32 + 10201 = 10169 10201 + 202u + u2 = 10169 Factor a perfect square on the left side: (u + 101)(u + 101) = 10169 Calculate the square root of the right side: 100.841459728 Break this problem into two subproblems by setting (u + 101) equal to 100.841459728 and -100.841459728.Subproblem 1
u + 101 = 100.841459728 Simplifying u + 101 = 100.841459728 Reorder the terms: 101 + u = 100.841459728 Solving 101 + u = 100.841459728 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-101' to each side of the equation. 101 + -101 + u = 100.841459728 + -101 Combine like terms: 101 + -101 = 0 0 + u = 100.841459728 + -101 u = 100.841459728 + -101 Combine like terms: 100.841459728 + -101 = -0.158540272 u = -0.158540272 Simplifying u = -0.158540272Subproblem 2
u + 101 = -100.841459728 Simplifying u + 101 = -100.841459728 Reorder the terms: 101 + u = -100.841459728 Solving 101 + u = -100.841459728 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-101' to each side of the equation. 101 + -101 + u = -100.841459728 + -101 Combine like terms: 101 + -101 = 0 0 + u = -100.841459728 + -101 u = -100.841459728 + -101 Combine like terms: -100.841459728 + -101 = -201.841459728 u = -201.841459728 Simplifying u = -201.841459728Solution
The solution to the problem is based on the solutions from the subproblems. u = {-0.158540272, -201.841459728}
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