0=x^2+21x-144

Solution for 0=x^2+21x-144 equation:

Simplifying
0 = x2 + 21x + -144

Reorder the terms:
0 = -144 + 21x + x2

Solving
0 = -144 + 21x + x2

Solving for variable 'x'.

Combine like terms: 0 + 144 = 144
144 + -21x + -1x2 = -144 + 21x + x2 + 144 + -21x + -1x2

Reorder the terms:
144 + -21x + -1x2 = -144 + 144 + 21x + -21x + x2 + -1x2

Combine like terms: -144 + 144 = 0
144 + -21x + -1x2 = 0 + 21x + -21x + x2 + -1x2
144 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
144 + -21x + -1x2 = 0 + x2 + -1x2
144 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
144 + -21x + -1x2 = 0

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

Divide each side by '-1'.
-144 + 21x + x2 = 0

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 21x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 21x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 21x + x2 = 0 + 144
21x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
21x + x2 = 144

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 144 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 144 + 110.25

Combine like terms: 144 + 110.25 = 254.25
110.25 + 21x + x2 = 254.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 254.25

Calculate the square root of the right side: 15.945218719

Break this problem into two subproblems by setting 
(x + 10.5) equal to 15.945218719 and -15.945218719.

Subproblem 1
x + 10.5 = 15.945218719

Simplifying
x + 10.5 = 15.945218719

Reorder the terms:
10.5 + x = 15.945218719

Solving
10.5 + x = 15.945218719

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 15.945218719 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 15.945218719 + -10.5
x = 15.945218719 + -10.5

Combine like terms: 15.945218719 + -10.5 = 5.445218719
x = 5.445218719

Simplifying
x = 5.445218719

Subproblem 2
x + 10.5 = -15.945218719

Simplifying
x + 10.5 = -15.945218719

Reorder the terms:
10.5 + x = -15.945218719

Solving
10.5 + x = -15.945218719

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -15.945218719 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -15.945218719 + -10.5
x = -15.945218719 + -10.5

Combine like terms: -15.945218719 + -10.5 = -26.445218719
x = -26.445218719

Simplifying
x = -26.445218719

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.445218719, -26.445218719}