6u^2+11u-24=

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Solution for 6u^2+11u-24= equation:


Simplifying
6u2 + 11u + -24 = 0

Reorder the terms:
-24 + 11u + 6u2 = 0

Solving
-24 + 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'.
-4 + 1.833333333u + u2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 1.833333333u + 4 + u2 = 0 + 4

Reorder the terms:
-4 + 4 + 1.833333333u + u2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 1.833333333u + u2 = 0 + 4
1.833333333u + u2 = 0 + 4

Combine like terms: 0 + 4 = 4
1.833333333u + u2 = 4

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 = 4 + 0.8402777775

Reorder the terms:
0.8402777775 + 1.833333333u + u2 = 4 + 0.8402777775

Combine like terms: 4 + 0.8402777775 = 4.8402777775
0.8402777775 + 1.833333333u + u2 = 4.8402777775

Factor a perfect square on the left side:
(u + 0.9166666665)(u + 0.9166666665) = 4.8402777775

Calculate the square root of the right side: 2.20006313

Break this problem into two subproblems by setting 
(u + 0.9166666665) equal to 2.20006313 and -2.20006313.

Subproblem 1

u + 0.9166666665 = 2.20006313 Simplifying u + 0.9166666665 = 2.20006313 Reorder the terms: 0.9166666665 + u = 2.20006313 Solving 0.9166666665 + u = 2.20006313 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 = 2.20006313 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + u = 2.20006313 + -0.9166666665 u = 2.20006313 + -0.9166666665 Combine like terms: 2.20006313 + -0.9166666665 = 1.2833964635 u = 1.2833964635 Simplifying u = 1.2833964635

Subproblem 2

u + 0.9166666665 = -2.20006313 Simplifying u + 0.9166666665 = -2.20006313 Reorder the terms: 0.9166666665 + u = -2.20006313 Solving 0.9166666665 + u = -2.20006313 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 = -2.20006313 + -0.9166666665 Combine like terms: 0.9166666665 + -0.9166666665 = 0.0000000000 0.0000000000 + u = -2.20006313 + -0.9166666665 u = -2.20006313 + -0.9166666665 Combine like terms: -2.20006313 + -0.9166666665 = -3.1167297965 u = -3.1167297965 Simplifying u = -3.1167297965

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.2833964635, -3.1167297965}

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