x^2+21x+100.25=0

Solution for x^2+21x+100.25=0 equation:

Simplifying
x2 + 21x + 100.25 = 0

Reorder the terms:
100.25 + 21x + x2 = 0

Solving
100.25 + 21x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-100.25' to each side of the equation.
100.25 + 21x + -100.25 + x2 = 0 + -100.25

Reorder the terms:
100.25 + -100.25 + 21x + x2 = 0 + -100.25

Combine like terms: 100.25 + -100.25 = 0.00
0.00 + 21x + x2 = 0 + -100.25
21x + x2 = 0 + -100.25

Combine like terms: 0 + -100.25 = -100.25
21x + x2 = -100.25

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 = -100.25 + 110.25

Reorder the terms:
110.25 + 21x + x2 = -100.25 + 110.25

Combine like terms: -100.25 + 110.25 = 10
110.25 + 21x + x2 = 10

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 10.5) equal to 3.16227766 and -3.16227766.

Subproblem 1
x + 10.5 = 3.16227766

Simplifying
x + 10.5 = 3.16227766

Reorder the terms:
10.5 + x = 3.16227766

Solving
10.5 + x = 3.16227766

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 = 3.16227766 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 3.16227766 + -10.5
x = 3.16227766 + -10.5

Combine like terms: 3.16227766 + -10.5 = -7.33772234
x = -7.33772234

Simplifying
x = -7.33772234

Subproblem 2
x + 10.5 = -3.16227766

Simplifying
x + 10.5 = -3.16227766

Reorder the terms:
10.5 + x = -3.16227766

Solving
10.5 + x = -3.16227766

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 = -3.16227766 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -3.16227766 + -10.5
x = -3.16227766 + -10.5

Combine like terms: -3.16227766 + -10.5 = -13.66227766
x = -13.66227766

Simplifying
x = -13.66227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.33772234, -13.66227766}