0=x^2+21x-2

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

Simplifying
0 = x2 + 21x + -2

Reorder the terms:
0 = -2 + 21x + x2

Solving
0 = -2 + 21x + x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -21x + -1x2 = -2 + 21x + x2 + 2 + -21x + -1x2

Reorder the terms:
2 + -21x + -1x2 = -2 + 2 + 21x + -21x + x2 + -1x2

Combine like terms: -2 + 2 = 0
2 + -21x + -1x2 = 0 + 21x + -21x + x2 + -1x2
2 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
2 + -21x + -1x2 = 0 + x2 + -1x2
2 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -21x + -1x2 = 0

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

Divide each side by '-1'.
-2 + 21x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 21x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 21x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 21x + x2 = 0 + 2
21x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
21x + x2 = 2

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 = 2 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 2 + 110.25

Combine like terms: 2 + 110.25 = 112.25
110.25 + 21x + x2 = 112.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 112.25

Calculate the square root of the right side: 10.59481005

Break this problem into two subproblems by setting 
(x + 10.5) equal to 10.59481005 and -10.59481005.

Subproblem 1
x + 10.5 = 10.59481005

Simplifying
x + 10.5 = 10.59481005

Reorder the terms:
10.5 + x = 10.59481005

Solving
10.5 + x = 10.59481005

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 = 10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 10.59481005 + -10.5
x = 10.59481005 + -10.5

Combine like terms: 10.59481005 + -10.5 = 0.09481005
x = 0.09481005

Simplifying
x = 0.09481005

Subproblem 2
x + 10.5 = -10.59481005

Simplifying
x + 10.5 = -10.59481005

Reorder the terms:
10.5 + x = -10.59481005

Solving
10.5 + x = -10.59481005

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 = -10.59481005 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -10.59481005 + -10.5
x = -10.59481005 + -10.5

Combine like terms: -10.59481005 + -10.5 = -21.09481005
x = -21.09481005

Simplifying
x = -21.09481005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.09481005, -21.09481005}