x^2+9x+20.25=19

Solution for x^2+9x+20.25=19 equation:

Simplifying
x2 + 9x + 20.25 = 19

Reorder the terms:
20.25 + 9x + x2 = 19

Solving
20.25 + 9x + x2 = 19

Solving for variable 'x'.

Reorder the terms:
20.25 + -19 + 9x + x2 = 19 + -19

Combine like terms: 20.25 + -19 = 1.25
1.25 + 9x + x2 = 19 + -19

Combine like terms: 19 + -19 = 0
1.25 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + 9x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + 9x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + 9x + x2 = 0 + -1.25
9x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
9x + x2 = -1.25

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -1.25 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -1.25 + 20.25

Combine like terms: -1.25 + 20.25 = 19
20.25 + 9x + x2 = 19

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.358898944 and -4.358898944.

Subproblem 1
x + 4.5 = 4.358898944

Simplifying
x + 4.5 = 4.358898944

Reorder the terms:
4.5 + x = 4.358898944

Solving
4.5 + x = 4.358898944

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 4.358898944 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.358898944 + -4.5
x = 4.358898944 + -4.5

Combine like terms: 4.358898944 + -4.5 = -0.141101056
x = -0.141101056

Simplifying
x = -0.141101056

Subproblem 2
x + 4.5 = -4.358898944

Simplifying
x + 4.5 = -4.358898944

Reorder the terms:
4.5 + x = -4.358898944

Solving
4.5 + x = -4.358898944

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -4.358898944 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.358898944 + -4.5
x = -4.358898944 + -4.5

Combine like terms: -4.358898944 + -4.5 = -8.858898944
x = -8.858898944

Simplifying
x = -8.858898944

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.141101056, -8.858898944}