x^2+19x+90.25=0

Solution for x^2+19x+90.25=0 equation:

Simplifying
x2 + 19x + 90.25 = 0

Reorder the terms:
90.25 + 19x + x2 = 0

Solving
90.25 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-90.25' to each side of the equation.
90.25 + 19x + -90.25 + x2 = 0 + -90.25

Reorder the terms:
90.25 + -90.25 + 19x + x2 = 0 + -90.25

Combine like terms: 90.25 + -90.25 = 0.00
0.00 + 19x + x2 = 0 + -90.25
19x + x2 = 0 + -90.25

Combine like terms: 0 + -90.25 = -90.25
19x + x2 = -90.25

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -90.25 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -90.25 + 90.25

Combine like terms: -90.25 + 90.25 = 0.00
90.25 + 19x + x2 = 0.00

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 9.5) equal to 0.00 and 0.00.

Subproblem 1
x + 9.5 = 0.00

Simplifying
x + 9.5 = 0.00

Reorder the terms:
9.5 + x = 0.00

Solving
9.5 + x = 0.00

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 0.00 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 0.00 + -9.5
x = 0.00 + -9.5

Combine like terms: 0.00 + -9.5 = -9.5
x = -9.5

Simplifying
x = -9.5

Subproblem 2
x + 9.5 = 0.00

Simplifying
x + 9.5 = 0.00

Reorder the terms:
9.5 + x = 0.00

Solving
9.5 + x = 0.00

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 0.00 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 0.00 + -9.5
x = 0.00 + -9.5

Combine like terms: 0.00 + -9.5 = -9.5
x = -9.5

Simplifying
x = -9.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-9.5, -9.5}