x^2+17x+72.25=0

Solution for x^2+17x+72.25=0 equation:

Simplifying
x2 + 17x + 72.25 = 0

Reorder the terms:
72.25 + 17x + x2 = 0

Solving
72.25 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-72.25' to each side of the equation.
72.25 + 17x + -72.25 + x2 = 0 + -72.25

Reorder the terms:
72.25 + -72.25 + 17x + x2 = 0 + -72.25

Combine like terms: 72.25 + -72.25 = 0.00
0.00 + 17x + x2 = 0 + -72.25
17x + x2 = 0 + -72.25

Combine like terms: 0 + -72.25 = -72.25
17x + x2 = -72.25

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = -72.25 + 72.25

Reorder the terms:
72.25 + 17x + x2 = -72.25 + 72.25

Combine like terms: -72.25 + 72.25 = 0.00
72.25 + 17x + x2 = 0.00

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 0.00

Calculate the square root of the right side: 0.00

Break this problem into two subproblems by setting 
(x + 8.5) equal to 0.00 and 0.00.

Subproblem 1
x + 8.5 = 0.00

Simplifying
x + 8.5 = 0.00

Reorder the terms:
8.5 + x = 0.00

Solving
8.5 + x = 0.00

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 0.00 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 0.00 + -8.5
x = 0.00 + -8.5

Combine like terms: 0.00 + -8.5 = -8.5
x = -8.5

Simplifying
x = -8.5

Subproblem 2
x + 8.5 = 0.00

Simplifying
x + 8.5 = 0.00

Reorder the terms:
8.5 + x = 0.00

Solving
8.5 + x = 0.00

Solving for variable 'x'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + x = 0.00 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 0.00 + -8.5
x = 0.00 + -8.5

Combine like terms: 0.00 + -8.5 = -8.5
x = -8.5

Simplifying
x = -8.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-8.5, -8.5}