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Simplifying u3 + -6u2 + -15u = 0 Reorder the terms: -15u + -6u2 + u3 = 0 Solving -15u + -6u2 + u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'u'. u(-15 + -6u + 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 '(-15 + -6u + u2)' equal to zero and attempt to solve: Simplifying -15 + -6u + u2 = 0 Solving -15 + -6u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -6u + 15 + u2 = 0 + 15 Reorder the terms: -15 + 15 + -6u + u2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -6u + u2 = 0 + 15 -6u + u2 = 0 + 15 Combine like terms: 0 + 15 = 15 -6u + u2 = 15 The u term is -6u. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6u + 9 + u2 = 15 + 9 Reorder the terms: 9 + -6u + u2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + -6u + u2 = 24 Factor a perfect square on the left side: (u + -3)(u + -3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (u + -3) equal to 4.898979486 and -4.898979486.Subproblem 1
u + -3 = 4.898979486 Simplifying u + -3 = 4.898979486 Reorder the terms: -3 + u = 4.898979486 Solving -3 + u = 4.898979486 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = 4.898979486 + 3 Combine like terms: -3 + 3 = 0 0 + u = 4.898979486 + 3 u = 4.898979486 + 3 Combine like terms: 4.898979486 + 3 = 7.898979486 u = 7.898979486 Simplifying u = 7.898979486Subproblem 2
u + -3 = -4.898979486 Simplifying u + -3 = -4.898979486 Reorder the terms: -3 + u = -4.898979486 Solving -3 + u = -4.898979486 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + u = -4.898979486 + 3 Combine like terms: -3 + 3 = 0 0 + u = -4.898979486 + 3 u = -4.898979486 + 3 Combine like terms: -4.898979486 + 3 = -1.898979486 u = -1.898979486 Simplifying u = -1.898979486Solution
The solution to the problem is based on the solutions from the subproblems. u = {7.898979486, -1.898979486}Solution
u = {0, 7.898979486, -1.898979486}
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