x^2-11x-15=0

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Solution for x^2-11x-15=0 equation: 


Simplifying
x2 + -11x + -15 = 0

Reorder the terms:
-15 + -11x + x2 = 0

Solving
-15 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -11x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -11x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -11x + x2 = 0 + 15
-11x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-11x + x2 = 15

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 = 15 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 15 + 30.25

Combine like terms: 15 + 30.25 = 45.25
30.25 + -11x + x2 = 45.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 45.25

Calculate the square root of the right side: 6.726812024

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.726812024 and -6.726812024.


Subproblem 1
x + -5.5 = 6.726812024

Simplifying
x + -5.5 = 6.726812024

Reorder the terms:
-5.5 + x = 6.726812024

Solving
-5.5 + x = 6.726812024

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 = 6.726812024 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.726812024 + 5.5
x = 6.726812024 + 5.5

Combine like terms: 6.726812024 + 5.5 = 12.226812024
x = 12.226812024

Simplifying
x = 12.226812024


Subproblem 2
x + -5.5 = -6.726812024

Simplifying
x + -5.5 = -6.726812024

Reorder the terms:
-5.5 + x = -6.726812024

Solving
-5.5 + x = -6.726812024

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 = -6.726812024 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.726812024 + 5.5
x = -6.726812024 + 5.5

Combine like terms: -6.726812024 + 5.5 = -1.226812024
x = -1.226812024

Simplifying
x = -1.226812024


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.226812024, -1.226812024}

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