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Simplifying u3 + -14u2 + 32u = 0 Reorder the terms: 32u + -14u2 + u3 = 0 Solving 32u + -14u2 + u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u'. u(32 + -14u + u2) = 0Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
Set the factor '(32 + -14u + u2)' equal to zero and attempt to solve: Simplifying 32 + -14u + u2 = 0 Solving 32 + -14u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -14u + -32 + u2 = 0 + -32 Reorder the terms: 32 + -32 + -14u + u2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -14u + u2 = 0 + -32 -14u + u2 = 0 + -32 Combine like terms: 0 + -32 = -32 -14u + u2 = -32 The u term is -14u. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14u + 49 + u2 = -32 + 49 Reorder the terms: 49 + -14u + u2 = -32 + 49 Combine like terms: -32 + 49 = 17 49 + -14u + u2 = 17 Factor a perfect square on the left side: (u + -7)(u + -7) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (u + -7) equal to 4.123105626 and -4.123105626.Subproblem 1
u + -7 = 4.123105626 Simplifying u + -7 = 4.123105626 Reorder the terms: -7 + u = 4.123105626 Solving -7 + u = 4.123105626 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = 4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + u = 4.123105626 + 7 u = 4.123105626 + 7 Combine like terms: 4.123105626 + 7 = 11.123105626 u = 11.123105626 Simplifying u = 11.123105626Subproblem 2
u + -7 = -4.123105626 Simplifying u + -7 = -4.123105626 Reorder the terms: -7 + u = -4.123105626 Solving -7 + u = -4.123105626 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + u = -4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + u = -4.123105626 + 7 u = -4.123105626 + 7 Combine like terms: -4.123105626 + 7 = 2.876894374 u = 2.876894374 Simplifying u = 2.876894374Solution
The solution to the problem is based on the solutions from the subproblems. u = {11.123105626, 2.876894374}Solution
u = {0, 11.123105626, 2.876894374}
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