0=x^2+121x-168

Solution for 0=x^2+121x-168 equation:

Simplifying
0 = x2 + 121x + -168

Reorder the terms:
0 = -168 + 121x + x2

Solving
0 = -168 + 121x + x2

Solving for variable 'x'.

Combine like terms: 0 + 168 = 168
168 + -121x + -1x2 = -168 + 121x + x2 + 168 + -121x + -1x2

Reorder the terms:
168 + -121x + -1x2 = -168 + 168 + 121x + -121x + x2 + -1x2

Combine like terms: -168 + 168 = 0
168 + -121x + -1x2 = 0 + 121x + -121x + x2 + -1x2
168 + -121x + -1x2 = 121x + -121x + x2 + -1x2

Combine like terms: 121x + -121x = 0
168 + -121x + -1x2 = 0 + x2 + -1x2
168 + -121x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
168 + -121x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-168 + 121x + x2 = 0

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + 121x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + 121x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + 121x + x2 = 0 + 168
121x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
121x + x2 = 168

The x term is 121x.  Take half its coefficient (60.5).
Square it (3660.25) and add it to both sides.

Add '3660.25' to each side of the equation.
121x + 3660.25 + x2 = 168 + 3660.25

Reorder the terms:
3660.25 + 121x + x2 = 168 + 3660.25

Combine like terms: 168 + 3660.25 = 3828.25
3660.25 + 121x + x2 = 3828.25

Factor a perfect square on the left side:
(x + 60.5)(x + 60.5) = 3828.25

Calculate the square root of the right side: 61.872853498

Break this problem into two subproblems by setting 
(x + 60.5) equal to 61.872853498 and -61.872853498.

Subproblem 1
x + 60.5 = 61.872853498

Simplifying
x + 60.5 = 61.872853498

Reorder the terms:
60.5 + x = 61.872853498

Solving
60.5 + x = 61.872853498

Solving for variable 'x'.

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

Add '-60.5' to each side of the equation.
60.5 + -60.5 + x = 61.872853498 + -60.5

Combine like terms: 60.5 + -60.5 = 0.0
0.0 + x = 61.872853498 + -60.5
x = 61.872853498 + -60.5

Combine like terms: 61.872853498 + -60.5 = 1.372853498
x = 1.372853498

Simplifying
x = 1.372853498

Subproblem 2
x + 60.5 = -61.872853498

Simplifying
x + 60.5 = -61.872853498

Reorder the terms:
60.5 + x = -61.872853498

Solving
60.5 + x = -61.872853498

Solving for variable 'x'.

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

Add '-60.5' to each side of the equation.
60.5 + -60.5 + x = -61.872853498 + -60.5

Combine like terms: 60.5 + -60.5 = 0.0
0.0 + x = -61.872853498 + -60.5
x = -61.872853498 + -60.5

Combine like terms: -61.872853498 + -60.5 = -122.372853498
x = -122.372853498

Simplifying
x = -122.372853498

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.372853498, -122.372853498}