9u^2-11u-6=0

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Solution for 9u^2-11u-6=0 equation:


Simplifying
9u2 + -11u + -6 = 0

Reorder the terms:
-6 + -11u + 9u2 = 0

Solving
-6 + -11u + 9u2 = 0

Solving for variable 'u'.

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

Divide each side by '9'.
-0.6666666667 + -1.222222222u + u2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1.222222222u + 0.6666666667 + u2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1.222222222u + u2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1.222222222u + u2 = 0 + 0.6666666667
-1.222222222u + u2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1.222222222u + u2 = 0.6666666667

The u term is -1.222222222u.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222u + 0.3734567900 + u2 = 0.6666666667 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222u + u2 = 0.6666666667 + 0.3734567900

Combine like terms: 0.6666666667 + 0.3734567900 = 1.0401234567
0.3734567900 + -1.222222222u + u2 = 1.0401234567

Factor a perfect square on the left side:
(u + -0.611111111)(u + -0.611111111) = 1.0401234567

Calculate the square root of the right side: 1.019864431

Break this problem into two subproblems by setting 
(u + -0.611111111) equal to 1.019864431 and -1.019864431.

Subproblem 1

u + -0.611111111 = 1.019864431 Simplifying u + -0.611111111 = 1.019864431 Reorder the terms: -0.611111111 + u = 1.019864431 Solving -0.611111111 + u = 1.019864431 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + u = 1.019864431 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + u = 1.019864431 + 0.611111111 u = 1.019864431 + 0.611111111 Combine like terms: 1.019864431 + 0.611111111 = 1.630975542 u = 1.630975542 Simplifying u = 1.630975542

Subproblem 2

u + -0.611111111 = -1.019864431 Simplifying u + -0.611111111 = -1.019864431 Reorder the terms: -0.611111111 + u = -1.019864431 Solving -0.611111111 + u = -1.019864431 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + u = -1.019864431 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + u = -1.019864431 + 0.611111111 u = -1.019864431 + 0.611111111 Combine like terms: -1.019864431 + 0.611111111 = -0.40875332 u = -0.40875332 Simplifying u = -0.40875332

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.630975542, -0.40875332}

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