x^2+11x-168=0

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Solution for x^2+11x-168=0 equation: 


Simplifying
x2 + 11x + -168 = 0

Reorder the terms:
-168 + 11x + x2 = 0

Solving
-168 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + 11x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + 11x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + 11x + x2 = 0 + 168
11x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
11x + x2 = 168

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 = 168 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 168 + 30.25

Combine like terms: 168 + 30.25 = 198.25
30.25 + 11x + x2 = 198.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 198.25

Calculate the square root of the right side: 14.08012784

Break this problem into two subproblems by setting 
(x + 5.5) equal to 14.08012784 and -14.08012784.


Subproblem 1
x + 5.5 = 14.08012784

Simplifying
x + 5.5 = 14.08012784

Reorder the terms:
5.5 + x = 14.08012784

Solving
5.5 + x = 14.08012784

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 = 14.08012784 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 14.08012784 + -5.5
x = 14.08012784 + -5.5

Combine like terms: 14.08012784 + -5.5 = 8.58012784
x = 8.58012784

Simplifying
x = 8.58012784


Subproblem 2
x + 5.5 = -14.08012784

Simplifying
x + 5.5 = -14.08012784

Reorder the terms:
5.5 + x = -14.08012784

Solving
5.5 + x = -14.08012784

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 = -14.08012784 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -14.08012784 + -5.5
x = -14.08012784 + -5.5

Combine like terms: -14.08012784 + -5.5 = -19.58012784
x = -19.58012784

Simplifying
x = -19.58012784


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.58012784, -19.58012784}

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