u^2-11u-18=0

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Solution for u^2-11u-18=0 equation: 


Simplifying
u2 + -11u + -18 = 0

Reorder the terms:
-18 + -11u + u2 = 0

Solving
-18 + -11u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -11u + 18 + u2 = 0 + 18

Reorder the terms:
-18 + 18 + -11u + u2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -11u + u2 = 0 + 18
-11u + u2 = 0 + 18

Combine like terms: 0 + 18 = 18
-11u + u2 = 18

The u term is -11u.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11u + 30.25 + u2 = 18 + 30.25

Reorder the terms:
30.25 + -11u + u2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + -11u + u2 = 48.25

Factor a perfect square on the left side:
(u + -5.5)(u + -5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(u + -5.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
u + -5.5 = 6.946221995

Simplifying
u + -5.5 = 6.946221995

Reorder the terms:
-5.5 + u = 6.946221995

Solving
-5.5 + u = 6.946221995

Solving for variable 'u'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + u = 6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + u = 6.946221995 + 5.5
u = 6.946221995 + 5.5

Combine like terms: 6.946221995 + 5.5 = 12.446221995
u = 12.446221995

Simplifying
u = 12.446221995


Subproblem 2
u + -5.5 = -6.946221995

Simplifying
u + -5.5 = -6.946221995

Reorder the terms:
-5.5 + u = -6.946221995

Solving
-5.5 + u = -6.946221995

Solving for variable 'u'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + u = -6.946221995 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + u = -6.946221995 + 5.5
u = -6.946221995 + 5.5

Combine like terms: -6.946221995 + 5.5 = -1.446221995
u = -1.446221995

Simplifying
u = -1.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {12.446221995, -1.446221995}

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