u^2-13u-21=0

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Solution for u^2-13u-21=0 equation: 


Simplifying
u2 + -13u + -21 = 0

Reorder the terms:
-21 + -13u + u2 = 0

Solving
-21 + -13u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -13u + 21 + u2 = 0 + 21

Reorder the terms:
-21 + 21 + -13u + u2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -13u + u2 = 0 + 21
-13u + u2 = 0 + 21

Combine like terms: 0 + 21 = 21
-13u + u2 = 21

The u term is -13u.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13u + 42.25 + u2 = 21 + 42.25

Reorder the terms:
42.25 + -13u + u2 = 21 + 42.25

Combine like terms: 21 + 42.25 = 63.25
42.25 + -13u + u2 = 63.25

Factor a perfect square on the left side:
(u + -6.5)(u + -6.5) = 63.25

Calculate the square root of the right side: 7.95298686

Break this problem into two subproblems by setting 
(u + -6.5) equal to 7.95298686 and -7.95298686.


Subproblem 1
u + -6.5 = 7.95298686

Simplifying
u + -6.5 = 7.95298686

Reorder the terms:
-6.5 + u = 7.95298686

Solving
-6.5 + u = 7.95298686

Solving for variable 'u'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + u = 7.95298686 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + u = 7.95298686 + 6.5
u = 7.95298686 + 6.5

Combine like terms: 7.95298686 + 6.5 = 14.45298686
u = 14.45298686

Simplifying
u = 14.45298686


Subproblem 2
u + -6.5 = -7.95298686

Simplifying
u + -6.5 = -7.95298686

Reorder the terms:
-6.5 + u = -7.95298686

Solving
-6.5 + u = -7.95298686

Solving for variable 'u'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + u = -7.95298686 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + u = -7.95298686 + 6.5
u = -7.95298686 + 6.5

Combine like terms: -7.95298686 + 6.5 = -1.45298686
u = -1.45298686

Simplifying
u = -1.45298686


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {14.45298686, -1.45298686}

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