x^2-4x-11=6

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Solution for x^2-4x-11=6 equation: 


Simplifying
x2 + -4x + -11 = 6

Reorder the terms:
-11 + -4x + x2 = 6

Solving
-11 + -4x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
-11 + -6 + -4x + x2 = 6 + -6

Combine like terms: -11 + -6 = -17
-17 + -4x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-17 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -4x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -4x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -4x + x2 = 0 + 17
-4x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-4x + x2 = 17

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 17 + 4

Reorder the terms:
4 + -4x + x2 = 17 + 4

Combine like terms: 17 + 4 = 21
4 + -4x + x2 = 21

Factor a perfect square on the left side:
(x + -2)(x + -2) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -2) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -2 = 4.582575695

Simplifying
x + -2 = 4.582575695

Reorder the terms:
-2 + x = 4.582575695

Solving
-2 + x = 4.582575695

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.582575695 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.582575695 + 2
x = 4.582575695 + 2

Combine like terms: 4.582575695 + 2 = 6.582575695
x = 6.582575695

Simplifying
x = 6.582575695


Subproblem 2
x + -2 = -4.582575695

Simplifying
x + -2 = -4.582575695

Reorder the terms:
-2 + x = -4.582575695

Solving
-2 + x = -4.582575695

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.582575695 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.582575695 + 2
x = -4.582575695 + 2

Combine like terms: -4.582575695 + 2 = -2.582575695
x = -2.582575695

Simplifying
x = -2.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.582575695, -2.582575695}

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