x^2+17x-144=0

Solution for x^2+17x-144=0 equation:

Simplifying
x2 + 17x + -144 = 0

Reorder the terms:
-144 + 17x + x2 = 0

Solving
-144 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 17x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 17x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 17x + x2 = 0 + 144
17x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
17x + x2 = 144

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 = 144 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 144 + 72.25

Combine like terms: 144 + 72.25 = 216.25
72.25 + 17x + x2 = 216.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 216.25

Calculate the square root of the right side: 14.70544117

Break this problem into two subproblems by setting 
(x + 8.5) equal to 14.70544117 and -14.70544117.

Subproblem 1
x + 8.5 = 14.70544117

Simplifying
x + 8.5 = 14.70544117

Reorder the terms:
8.5 + x = 14.70544117

Solving
8.5 + x = 14.70544117

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 = 14.70544117 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 14.70544117 + -8.5
x = 14.70544117 + -8.5

Combine like terms: 14.70544117 + -8.5 = 6.20544117
x = 6.20544117

Simplifying
x = 6.20544117

Subproblem 2
x + 8.5 = -14.70544117

Simplifying
x + 8.5 = -14.70544117

Reorder the terms:
8.5 + x = -14.70544117

Solving
8.5 + x = -14.70544117

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 = -14.70544117 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -14.70544117 + -8.5
x = -14.70544117 + -8.5

Combine like terms: -14.70544117 + -8.5 = -23.20544117
x = -23.20544117

Simplifying
x = -23.20544117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.20544117, -23.20544117}