a^2-11a-36=0

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Solution for a^2-11a-36=0 equation: 


Simplifying
a2 + -11a + -36 = 0

Reorder the terms:
-36 + -11a + a2 = 0

Solving
-36 + -11a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -11a + 36 + a2 = 0 + 36

Reorder the terms:
-36 + 36 + -11a + a2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -11a + a2 = 0 + 36
-11a + a2 = 0 + 36

Combine like terms: 0 + 36 = 36
-11a + a2 = 36

The a term is -11a.  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.
-11a + 30.25 + a2 = 36 + 30.25

Reorder the terms:
30.25 + -11a + a2 = 36 + 30.25

Combine like terms: 36 + 30.25 = 66.25
30.25 + -11a + a2 = 66.25

Factor a perfect square on the left side:
(a + -5.5)(a + -5.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(a + -5.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
a + -5.5 = 8.139410298

Simplifying
a + -5.5 = 8.139410298

Reorder the terms:
-5.5 + a = 8.139410298

Solving
-5.5 + a = 8.139410298

Solving for variable 'a'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + a = 8.139410298 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + a = 8.139410298 + 5.5
a = 8.139410298 + 5.5

Combine like terms: 8.139410298 + 5.5 = 13.639410298
a = 13.639410298

Simplifying
a = 13.639410298


Subproblem 2
a + -5.5 = -8.139410298

Simplifying
a + -5.5 = -8.139410298

Reorder the terms:
-5.5 + a = -8.139410298

Solving
-5.5 + a = -8.139410298

Solving for variable 'a'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + a = -8.139410298 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + a = -8.139410298 + 5.5
a = -8.139410298 + 5.5

Combine like terms: -8.139410298 + 5.5 = -2.639410298
a = -2.639410298

Simplifying
a = -2.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {13.639410298, -2.639410298}

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