x^2+3x-106=0

Solution for x^2+3x-106=0 equation:

Simplifying
x2 + 3x + -106 = 0

Reorder the terms:
-106 + 3x + x2 = 0

Solving
-106 + 3x + 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 + 3x + 106 + x2 = 0 + 106

Reorder the terms:
-106 + 106 + 3x + x2 = 0 + 106

Combine like terms: -106 + 106 = 0
0 + 3x + x2 = 0 + 106
3x + x2 = 0 + 106

Combine like terms: 0 + 106 = 106
3x + x2 = 106

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 106 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 106 + 2.25

Combine like terms: 106 + 2.25 = 108.25
2.25 + 3x + x2 = 108.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 108.25

Calculate the square root of the right side: 10.404326023

Break this problem into two subproblems by setting 
(x + 1.5) equal to 10.404326023 and -10.404326023.

Subproblem 1
x + 1.5 = 10.404326023

Simplifying
x + 1.5 = 10.404326023

Reorder the terms:
1.5 + x = 10.404326023

Solving
1.5 + x = 10.404326023

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 10.404326023 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 10.404326023 + -1.5
x = 10.404326023 + -1.5

Combine like terms: 10.404326023 + -1.5 = 8.904326023
x = 8.904326023

Simplifying
x = 8.904326023

Subproblem 2
x + 1.5 = -10.404326023

Simplifying
x + 1.5 = -10.404326023

Reorder the terms:
1.5 + x = -10.404326023

Solving
1.5 + x = -10.404326023

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -10.404326023 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -10.404326023 + -1.5
x = -10.404326023 + -1.5

Combine like terms: -10.404326023 + -1.5 = -11.904326023
x = -11.904326023

Simplifying
x = -11.904326023

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.904326023, -11.904326023}