x^2-5x-11=0

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Solution for x^2-5x-11=0 equation: 


Simplifying
x2 + -5x + -11 = 0

Reorder the terms:
-11 + -5x + x2 = 0

Solving
-11 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -5x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -5x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -5x + x2 = 0 + 11
-5x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-5x + x2 = 11

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 11 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 11 + 6.25

Combine like terms: 11 + 6.25 = 17.25
6.25 + -5x + x2 = 17.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + -2.5 = 4.153311931

Simplifying
x + -2.5 = 4.153311931

Reorder the terms:
-2.5 + x = 4.153311931

Solving
-2.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.153311931 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.153311931 + 2.5
x = 4.153311931 + 2.5

Combine like terms: 4.153311931 + 2.5 = 6.653311931
x = 6.653311931

Simplifying
x = 6.653311931


Subproblem 2
x + -2.5 = -4.153311931

Simplifying
x + -2.5 = -4.153311931

Reorder the terms:
-2.5 + x = -4.153311931

Solving
-2.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.153311931 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.153311931 + 2.5
x = -4.153311931 + 2.5

Combine like terms: -4.153311931 + 2.5 = -1.653311931
x = -1.653311931

Simplifying
x = -1.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.653311931, -1.653311931}

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