6u^2+11u-41=0

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Solution for 6u^2+11u-41=0 equation: 


Simplifying
6u2 + 11u + -41 = 0

Reorder the terms:
-41 + 11u + 6u2 = 0

Solving
-41 + 11u + 6u2 = 0

Solving for variable 'u'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-6.833333333 + 1.833333333u + u2 = 0

Move the constant term to the right:

Add '6.833333333' to each side of the equation.
-6.833333333 + 1.833333333u + 6.833333333 + u2 = 0 + 6.833333333

Reorder the terms:
-6.833333333 + 6.833333333 + 1.833333333u + u2 = 0 + 6.833333333

Combine like terms: -6.833333333 + 6.833333333 = 0.000000000
0.000000000 + 1.833333333u + u2 = 0 + 6.833333333
1.833333333u + u2 = 0 + 6.833333333

Combine like terms: 0 + 6.833333333 = 6.833333333
1.833333333u + u2 = 6.833333333

The u term is 1.833333333u.  Take half its coefficient (0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
1.833333333u + 0.8402777775 + u2 = 6.833333333 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333u + u2 = 6.833333333 + 0.8402777775

Combine like terms: 6.833333333 + 0.8402777775 = 7.6736111105
0.8402777775 + 1.833333333u + u2 = 7.6736111105

Factor a perfect square on the left side:
(u + 0.9166666665)(u + 0.9166666665) = 7.6736111105

Calculate the square root of the right side: 2.770128356

Break this problem into two subproblems by setting 
(u + 0.9166666665) equal to 2.770128356 and -2.770128356.


Subproblem 1
u + 0.9166666665 = 2.770128356

Simplifying
u + 0.9166666665 = 2.770128356

Reorder the terms:
0.9166666665 + u = 2.770128356

Solving
0.9166666665 + u = 2.770128356

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + u = 2.770128356 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + u = 2.770128356 + -0.9166666665
u = 2.770128356 + -0.9166666665

Combine like terms: 2.770128356 + -0.9166666665 = 1.8534616895
u = 1.8534616895

Simplifying
u = 1.8534616895


Subproblem 2
u + 0.9166666665 = -2.770128356

Simplifying
u + 0.9166666665 = -2.770128356

Reorder the terms:
0.9166666665 + u = -2.770128356

Solving
0.9166666665 + u = -2.770128356

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '-0.9166666665' to each side of the equation.
0.9166666665 + -0.9166666665 + u = -2.770128356 + -0.9166666665

Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000
0.0000000000 + u = -2.770128356 + -0.9166666665
u = -2.770128356 + -0.9166666665

Combine like terms: -2.770128356 + -0.9166666665 = -3.6867950225
u = -3.6867950225

Simplifying
u = -3.6867950225


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {1.8534616895, -3.6867950225}

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