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Simplifying 2u3 + 5u2 + -50u = 0 Reorder the terms: -50u + 5u2 + 2u3 = 0 Solving -50u + 5u2 + 2u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u'. u(-50 + 5u + 2u2) = 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 '(-50 + 5u + 2u2)' equal to zero and attempt to solve: Simplifying -50 + 5u + 2u2 = 0 Solving -50 + 5u + 2u2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25 + 2.5u + u2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 2.5u + 25 + u2 = 0 + 25 Reorder the terms: -25 + 25 + 2.5u + u2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2.5u + u2 = 0 + 25 2.5u + u2 = 0 + 25 Combine like terms: 0 + 25 = 25 2.5u + u2 = 25 The u term is 2.5u. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5u + 1.5625 + u2 = 25 + 1.5625 Reorder the terms: 1.5625 + 2.5u + u2 = 25 + 1.5625 Combine like terms: 25 + 1.5625 = 26.5625 1.5625 + 2.5u + u2 = 26.5625 Factor a perfect square on the left side: (u + 1.25)(u + 1.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (u + 1.25) equal to 5.153882032 and -5.153882032.Subproblem 1
u + 1.25 = 5.153882032 Simplifying u + 1.25 = 5.153882032 Reorder the terms: 1.25 + u = 5.153882032 Solving 1.25 + u = 5.153882032 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + u = 5.153882032 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + u = 5.153882032 + -1.25 u = 5.153882032 + -1.25 Combine like terms: 5.153882032 + -1.25 = 3.903882032 u = 3.903882032 Simplifying u = 3.903882032Subproblem 2
u + 1.25 = -5.153882032 Simplifying u + 1.25 = -5.153882032 Reorder the terms: 1.25 + u = -5.153882032 Solving 1.25 + u = -5.153882032 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + u = -5.153882032 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + u = -5.153882032 + -1.25 u = -5.153882032 + -1.25 Combine like terms: -5.153882032 + -1.25 = -6.403882032 u = -6.403882032 Simplifying u = -6.403882032Solution
The solution to the problem is based on the solutions from the subproblems. u = {3.903882032, -6.403882032}Solution
u = {0, 3.903882032, -6.403882032}
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