2x^2+13x=2+6

Solution for 2x^2+13x=2+6 equation:

Simplifying
2x2 + 13x = 2 + 6

Reorder the terms:
13x + 2x2 = 2 + 6

Combine like terms: 2 + 6 = 8
13x + 2x2 = 8

Solving
13x + 2x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 13x + 2x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 13x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-4 + 6.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 6.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 6.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 6.5x + x2 = 0 + 4
6.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
6.5x + x2 = 4

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 4 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 4 + 10.5625

Combine like terms: 4 + 10.5625 = 14.5625
10.5625 + 6.5x + x2 = 14.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(x + 3.25) equal to 3.816084381 and -3.816084381.

Subproblem 1
x + 3.25 = 3.816084381

Simplifying
x + 3.25 = 3.816084381

Reorder the terms:
3.25 + x = 3.816084381

Solving
3.25 + x = 3.816084381

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 3.816084381 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 3.816084381 + -3.25
x = 3.816084381 + -3.25

Combine like terms: 3.816084381 + -3.25 = 0.566084381
x = 0.566084381

Simplifying
x = 0.566084381

Subproblem 2
x + 3.25 = -3.816084381

Simplifying
x + 3.25 = -3.816084381

Reorder the terms:
3.25 + x = -3.816084381

Solving
3.25 + x = -3.816084381

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -3.816084381 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -3.816084381 + -3.25
x = -3.816084381 + -3.25

Combine like terms: -3.816084381 + -3.25 = -7.066084381
x = -7.066084381

Simplifying
x = -7.066084381

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.566084381, -7.066084381}