2x^2+102x-106=0

Solution for 2x^2+102x-106=0 equation:

Simplifying
2x2 + 102x + -106 = 0

Reorder the terms:
-106 + 102x + 2x2 = 0

Solving
-106 + 102x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-53 + 51x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-53 + 51x + x2)' equal to zero and attempt to solve:

Simplifying
-53 + 51x + x2 = 0

Solving
-53 + 51x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + 51x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + 51x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + 51x + x2 = 0 + 53
51x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
51x + x2 = 53

The x term is 51x.  Take half its coefficient (25.5).
Square it (650.25) and add it to both sides.

Add '650.25' to each side of the equation.
51x + 650.25 + x2 = 53 + 650.25

Reorder the terms:
650.25 + 51x + x2 = 53 + 650.25

Combine like terms: 53 + 650.25 = 703.25
650.25 + 51x + x2 = 703.25

Factor a perfect square on the left side:
(x + 25.5)(x + 25.5) = 703.25

Calculate the square root of the right side: 26.518861212

Break this problem into two subproblems by setting 
(x + 25.5) equal to 26.518861212 and -26.518861212.

Subproblem 1
x + 25.5 = 26.518861212

Simplifying
x + 25.5 = 26.518861212

Reorder the terms:
25.5 + x = 26.518861212

Solving
25.5 + x = 26.518861212

Solving for variable 'x'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + x = 26.518861212 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + x = 26.518861212 + -25.5
x = 26.518861212 + -25.5

Combine like terms: 26.518861212 + -25.5 = 1.018861212
x = 1.018861212

Simplifying
x = 1.018861212

Subproblem 2
x + 25.5 = -26.518861212

Simplifying
x + 25.5 = -26.518861212

Reorder the terms:
25.5 + x = -26.518861212

Solving
25.5 + x = -26.518861212

Solving for variable 'x'.

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

Add '-25.5' to each side of the equation.
25.5 + -25.5 + x = -26.518861212 + -25.5

Combine like terms: 25.5 + -25.5 = 0.0
0.0 + x = -26.518861212 + -25.5
x = -26.518861212 + -25.5

Combine like terms: -26.518861212 + -25.5 = -52.018861212
x = -52.018861212

Simplifying
x = -52.018861212

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.018861212, -52.018861212}
Solution
x = {1.018861212, -52.018861212}