X^2-11X-20=0

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Solution for X^2-11X-20=0 equation: 


Simplifying
X2 + -11X + -20 = 0

Reorder the terms:
-20 + -11X + X2 = 0

Solving
-20 + -11X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -11X + 20 + X2 = 0 + 20

Reorder the terms:
-20 + 20 + -11X + X2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -11X + X2 = 0 + 20
-11X + X2 = 0 + 20

Combine like terms: 0 + 20 = 20
-11X + X2 = 20

The X term is -11X.  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.
-11X + 30.25 + X2 = 20 + 30.25

Reorder the terms:
30.25 + -11X + X2 = 20 + 30.25

Combine like terms: 20 + 30.25 = 50.25
30.25 + -11X + X2 = 50.25

Factor a perfect square on the left side:
(X + -5.5)(X + -5.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(X + -5.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
X + -5.5 = 7.088723439

Simplifying
X + -5.5 = 7.088723439

Reorder the terms:
-5.5 + X = 7.088723439

Solving
-5.5 + X = 7.088723439

Solving for variable 'X'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + X = 7.088723439 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + X = 7.088723439 + 5.5
X = 7.088723439 + 5.5

Combine like terms: 7.088723439 + 5.5 = 12.588723439
X = 12.588723439

Simplifying
X = 12.588723439


Subproblem 2
X + -5.5 = -7.088723439

Simplifying
X + -5.5 = -7.088723439

Reorder the terms:
-5.5 + X = -7.088723439

Solving
-5.5 + X = -7.088723439

Solving for variable 'X'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + X = -7.088723439 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + X = -7.088723439 + 5.5
X = -7.088723439 + 5.5

Combine like terms: -7.088723439 + 5.5 = -1.588723439
X = -1.588723439

Simplifying
X = -1.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {12.588723439, -1.588723439}

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