u^2-13.4u-32.56=0

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Solution for u^2-13.4u-32.56=0 equation: 


Simplifying
u2 + -13.4u + -32.56 = 0

Reorder the terms:
-32.56 + -13.4u + u2 = 0

Solving
-32.56 + -13.4u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '32.56' to each side of the equation.
-32.56 + -13.4u + 32.56 + u2 = 0 + 32.56

Reorder the terms:
-32.56 + 32.56 + -13.4u + u2 = 0 + 32.56

Combine like terms: -32.56 + 32.56 = 0.00
0.00 + -13.4u + u2 = 0 + 32.56
-13.4u + u2 = 0 + 32.56

Combine like terms: 0 + 32.56 = 32.56
-13.4u + u2 = 32.56

The u term is -13.4u.  Take half its coefficient (-6.7).
Square it (44.89) and add it to both sides.

Add '44.89' to each side of the equation.
-13.4u + 44.89 + u2 = 32.56 + 44.89

Reorder the terms:
44.89 + -13.4u + u2 = 32.56 + 44.89

Combine like terms: 32.56 + 44.89 = 77.45
44.89 + -13.4u + u2 = 77.45

Factor a perfect square on the left side:
(u + -6.7)(u + -6.7) = 77.45

Calculate the square root of the right side: 8.800568163

Break this problem into two subproblems by setting 
(u + -6.7) equal to 8.800568163 and -8.800568163.


Subproblem 1
u + -6.7 = 8.800568163

Simplifying
u + -6.7 = 8.800568163

Reorder the terms:
-6.7 + u = 8.800568163

Solving
-6.7 + u = 8.800568163

Solving for variable 'u'.

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

Add '6.7' to each side of the equation.
-6.7 + 6.7 + u = 8.800568163 + 6.7

Combine like terms: -6.7 + 6.7 = 0.0
0.0 + u = 8.800568163 + 6.7
u = 8.800568163 + 6.7

Combine like terms: 8.800568163 + 6.7 = 15.500568163
u = 15.500568163

Simplifying
u = 15.500568163


Subproblem 2
u + -6.7 = -8.800568163

Simplifying
u + -6.7 = -8.800568163

Reorder the terms:
-6.7 + u = -8.800568163

Solving
-6.7 + u = -8.800568163

Solving for variable 'u'.

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

Add '6.7' to each side of the equation.
-6.7 + 6.7 + u = -8.800568163 + 6.7

Combine like terms: -6.7 + 6.7 = 0.0
0.0 + u = -8.800568163 + 6.7
u = -8.800568163 + 6.7

Combine like terms: -8.800568163 + 6.7 = -2.100568163
u = -2.100568163

Simplifying
u = -2.100568163


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {15.500568163, -2.100568163}

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