a^2-13a-22=0

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Solution for a^2-13a-22=0 equation: 


Simplifying
a2 + -13a + -22 = 0

Reorder the terms:
-22 + -13a + a2 = 0

Solving
-22 + -13a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -13a + 22 + a2 = 0 + 22

Reorder the terms:
-22 + 22 + -13a + a2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -13a + a2 = 0 + 22
-13a + a2 = 0 + 22

Combine like terms: 0 + 22 = 22
-13a + a2 = 22

The a term is -13a.  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.
-13a + 42.25 + a2 = 22 + 42.25

Reorder the terms:
42.25 + -13a + a2 = 22 + 42.25

Combine like terms: 22 + 42.25 = 64.25
42.25 + -13a + a2 = 64.25

Factor a perfect square on the left side:
(a + -6.5)(a + -6.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(a + -6.5) equal to 8.015609771 and -8.015609771.


Subproblem 1
a + -6.5 = 8.015609771

Simplifying
a + -6.5 = 8.015609771

Reorder the terms:
-6.5 + a = 8.015609771

Solving
-6.5 + a = 8.015609771

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = 8.015609771 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = 8.015609771 + 6.5
a = 8.015609771 + 6.5

Combine like terms: 8.015609771 + 6.5 = 14.515609771
a = 14.515609771

Simplifying
a = 14.515609771


Subproblem 2
a + -6.5 = -8.015609771

Simplifying
a + -6.5 = -8.015609771

Reorder the terms:
-6.5 + a = -8.015609771

Solving
-6.5 + a = -8.015609771

Solving for variable 'a'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + a = -8.015609771 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + a = -8.015609771 + 6.5
a = -8.015609771 + 6.5

Combine like terms: -8.015609771 + 6.5 = -1.515609771
a = -1.515609771

Simplifying
a = -1.515609771


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {14.515609771, -1.515609771}

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