x^2+19x-106=0

Solution for x^2+19x-106=0 equation:

Simplifying
x2 + 19x + -106 = 0

Reorder the terms:
-106 + 19x + x2 = 0

Solving
-106 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '106' to each side of the equation.
-106 + 19x + 106 + x2 = 0 + 106

Reorder the terms:
-106 + 106 + 19x + x2 = 0 + 106

Combine like terms: -106 + 106 = 0
0 + 19x + x2 = 0 + 106
19x + x2 = 0 + 106

Combine like terms: 0 + 106 = 106
19x + x2 = 106

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 = 106 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 106 + 90.25

Combine like terms: 106 + 90.25 = 196.25
90.25 + 19x + x2 = 196.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 196.25

Calculate the square root of the right side: 14.008925726

Break this problem into two subproblems by setting 
(x + 9.5) equal to 14.008925726 and -14.008925726.

Subproblem 1
x + 9.5 = 14.008925726

Simplifying
x + 9.5 = 14.008925726

Reorder the terms:
9.5 + x = 14.008925726

Solving
9.5 + x = 14.008925726

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 = 14.008925726 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 14.008925726 + -9.5
x = 14.008925726 + -9.5

Combine like terms: 14.008925726 + -9.5 = 4.508925726
x = 4.508925726

Simplifying
x = 4.508925726

Subproblem 2
x + 9.5 = -14.008925726

Simplifying
x + 9.5 = -14.008925726

Reorder the terms:
9.5 + x = -14.008925726

Solving
9.5 + x = -14.008925726

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 = -14.008925726 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -14.008925726 + -9.5
x = -14.008925726 + -9.5

Combine like terms: -14.008925726 + -9.5 = -23.508925726
x = -23.508925726

Simplifying
x = -23.508925726

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.508925726, -23.508925726}