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Simplifying 3u2 + -36u + -111 = 0 Reorder the terms: -111 + -36u + 3u2 = 0 Solving -111 + -36u + 3u2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(-37 + -12u + u2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-37 + -12u + u2)' equal to zero and attempt to solve: Simplifying -37 + -12u + u2 = 0 Solving -37 + -12u + u2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -12u + 37 + u2 = 0 + 37 Reorder the terms: -37 + 37 + -12u + u2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -12u + u2 = 0 + 37 -12u + u2 = 0 + 37 Combine like terms: 0 + 37 = 37 -12u + u2 = 37 The u term is -12u. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12u + 36 + u2 = 37 + 36 Reorder the terms: 36 + -12u + u2 = 37 + 36 Combine like terms: 37 + 36 = 73 36 + -12u + u2 = 73 Factor a perfect square on the left side: (u + -6)(u + -6) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (u + -6) equal to 8.544003745 and -8.544003745.Subproblem 1
u + -6 = 8.544003745 Simplifying u + -6 = 8.544003745 Reorder the terms: -6 + u = 8.544003745 Solving -6 + u = 8.544003745 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = 8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + u = 8.544003745 + 6 u = 8.544003745 + 6 Combine like terms: 8.544003745 + 6 = 14.544003745 u = 14.544003745 Simplifying u = 14.544003745Subproblem 2
u + -6 = -8.544003745 Simplifying u + -6 = -8.544003745 Reorder the terms: -6 + u = -8.544003745 Solving -6 + u = -8.544003745 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + u = -8.544003745 + 6 Combine like terms: -6 + 6 = 0 0 + u = -8.544003745 + 6 u = -8.544003745 + 6 Combine like terms: -8.544003745 + 6 = -2.544003745 u = -2.544003745 Simplifying u = -2.544003745Solution
The solution to the problem is based on the solutions from the subproblems. u = {14.544003745, -2.544003745}Solution
u = {14.544003745, -2.544003745}
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