X^2+13X-89=0

Solution for X^2+13X-89=0 equation:

Simplifying
X2 + 13X + -89 = 0

Reorder the terms:
-89 + 13X + X2 = 0

Solving
-89 + 13X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + 13X + 89 + X2 = 0 + 89

Reorder the terms:
-89 + 89 + 13X + X2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + 13X + X2 = 0 + 89
13X + X2 = 0 + 89

Combine like terms: 0 + 89 = 89
13X + X2 = 89

The X term is 13X.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13X + 42.25 + X2 = 89 + 42.25

Reorder the terms:
42.25 + 13X + X2 = 89 + 42.25

Combine like terms: 89 + 42.25 = 131.25
42.25 + 13X + X2 = 131.25

Factor a perfect square on the left side:
(X + 6.5)(X + 6.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(X + 6.5) equal to 11.456439237 and -11.456439237.

Subproblem 1
X + 6.5 = 11.456439237

Simplifying
X + 6.5 = 11.456439237

Reorder the terms:
6.5 + X = 11.456439237

Solving
6.5 + X = 11.456439237

Solving for variable 'X'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + X = 11.456439237 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + X = 11.456439237 + -6.5
X = 11.456439237 + -6.5

Combine like terms: 11.456439237 + -6.5 = 4.956439237
X = 4.956439237

Simplifying
X = 4.956439237

Subproblem 2
X + 6.5 = -11.456439237

Simplifying
X + 6.5 = -11.456439237

Reorder the terms:
6.5 + X = -11.456439237

Solving
6.5 + X = -11.456439237

Solving for variable 'X'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + X = -11.456439237 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + X = -11.456439237 + -6.5
X = -11.456439237 + -6.5

Combine like terms: -11.456439237 + -6.5 = -17.956439237
X = -17.956439237

Simplifying
X = -17.956439237

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {4.956439237, -17.956439237}