u^2-10u-13=0

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Solution for u^2-10u-13=0 equation: 


Simplifying
u2 + -10u + -13 = 0

Reorder the terms:
-13 + -10u + u2 = 0

Solving
-13 + -10u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -10u + 13 + u2 = 0 + 13

Reorder the terms:
-13 + 13 + -10u + u2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -10u + u2 = 0 + 13
-10u + u2 = 0 + 13

Combine like terms: 0 + 13 = 13
-10u + u2 = 13

The u term is -10u.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10u + 25 + u2 = 13 + 25

Reorder the terms:
25 + -10u + u2 = 13 + 25

Combine like terms: 13 + 25 = 38
25 + -10u + u2 = 38

Factor a perfect square on the left side:
(u + -5)(u + -5) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(u + -5) equal to 6.164414003 and -6.164414003.


Subproblem 1
u + -5 = 6.164414003

Simplifying
u + -5 = 6.164414003

Reorder the terms:
-5 + u = 6.164414003

Solving
-5 + u = 6.164414003

Solving for variable 'u'.

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

Add '5' to each side of the equation.
-5 + 5 + u = 6.164414003 + 5

Combine like terms: -5 + 5 = 0
0 + u = 6.164414003 + 5
u = 6.164414003 + 5

Combine like terms: 6.164414003 + 5 = 11.164414003
u = 11.164414003

Simplifying
u = 11.164414003


Subproblem 2
u + -5 = -6.164414003

Simplifying
u + -5 = -6.164414003

Reorder the terms:
-5 + u = -6.164414003

Solving
-5 + u = -6.164414003

Solving for variable 'u'.

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

Add '5' to each side of the equation.
-5 + 5 + u = -6.164414003 + 5

Combine like terms: -5 + 5 = 0
0 + u = -6.164414003 + 5
u = -6.164414003 + 5

Combine like terms: -6.164414003 + 5 = -1.164414003
u = -1.164414003

Simplifying
u = -1.164414003


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {11.164414003, -1.164414003}

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