441=x^2+21x

Solution for 441=x^2+21x equation:

Simplifying
441 = x2 + 21x

Reorder the terms:
441 = 21x + x2

Solving
441 = 21x + x2

Solving for variable 'x'.

Reorder the terms:
441 + -21x + -1x2 = 21x + -21x + x2 + -1x2

Combine like terms: 21x + -21x = 0
441 + -21x + -1x2 = 0 + x2 + -1x2
441 + -21x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
441 + -21x + -1x2 = 0

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

Divide each side by '-1'.
-441 + 21x + x2 = 0

Move the constant term to the right:

Add '441' to each side of the equation.
-441 + 21x + 441 + x2 = 0 + 441

Reorder the terms:
-441 + 441 + 21x + x2 = 0 + 441

Combine like terms: -441 + 441 = 0
0 + 21x + x2 = 0 + 441
21x + x2 = 0 + 441

Combine like terms: 0 + 441 = 441
21x + x2 = 441

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 = 441 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 441 + 110.25

Combine like terms: 441 + 110.25 = 551.25
110.25 + 21x + x2 = 551.25

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 551.25

Calculate the square root of the right side: 23.478713764

Break this problem into two subproblems by setting 
(x + 10.5) equal to 23.478713764 and -23.478713764.

Subproblem 1
x + 10.5 = 23.478713764

Simplifying
x + 10.5 = 23.478713764

Reorder the terms:
10.5 + x = 23.478713764

Solving
10.5 + x = 23.478713764

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 = 23.478713764 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 23.478713764 + -10.5
x = 23.478713764 + -10.5

Combine like terms: 23.478713764 + -10.5 = 12.978713764
x = 12.978713764

Simplifying
x = 12.978713764

Subproblem 2
x + 10.5 = -23.478713764

Simplifying
x + 10.5 = -23.478713764

Reorder the terms:
10.5 + x = -23.478713764

Solving
10.5 + x = -23.478713764

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 = -23.478713764 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -23.478713764 + -10.5
x = -23.478713764 + -10.5

Combine like terms: -23.478713764 + -10.5 = -33.978713764
x = -33.978713764

Simplifying
x = -33.978713764

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.978713764, -33.978713764}