195=2x^2+13x+4

Solution for 195=2x^2+13x+4 equation:

Simplifying
195 = 2x2 + 13x + 4

Reorder the terms:
195 = 4 + 13x + 2x2

Solving
195 = 4 + 13x + 2x2

Solving for variable 'x'.

Combine like terms: 195 + -4 = 191
191 + -13x + -2x2 = 4 + 13x + 2x2 + -4 + -13x + -2x2

Reorder the terms:
191 + -13x + -2x2 = 4 + -4 + 13x + -13x + 2x2 + -2x2

Combine like terms: 4 + -4 = 0
191 + -13x + -2x2 = 0 + 13x + -13x + 2x2 + -2x2
191 + -13x + -2x2 = 13x + -13x + 2x2 + -2x2

Combine like terms: 13x + -13x = 0
191 + -13x + -2x2 = 0 + 2x2 + -2x2
191 + -13x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
191 + -13x + -2x2 = 0

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

Divide each side by '-2'.
-95.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '95.5' to each side of the equation.
-95.5 + 6.5x + 95.5 + x2 = 0 + 95.5

Reorder the terms:
-95.5 + 95.5 + 6.5x + x2 = 0 + 95.5

Combine like terms: -95.5 + 95.5 = 0.0
0.0 + 6.5x + x2 = 0 + 95.5
6.5x + x2 = 0 + 95.5

Combine like terms: 0 + 95.5 = 95.5
6.5x + x2 = 95.5

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 = 95.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 95.5 + 10.5625

Combine like terms: 95.5 + 10.5625 = 106.0625
10.5625 + 6.5x + x2 = 106.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 106.0625

Calculate the square root of the right side: 10.298664962

Break this problem into two subproblems by setting 
(x + 3.25) equal to 10.298664962 and -10.298664962.

Subproblem 1
x + 3.25 = 10.298664962

Simplifying
x + 3.25 = 10.298664962

Reorder the terms:
3.25 + x = 10.298664962

Solving
3.25 + x = 10.298664962

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 = 10.298664962 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 10.298664962 + -3.25
x = 10.298664962 + -3.25

Combine like terms: 10.298664962 + -3.25 = 7.048664962
x = 7.048664962

Simplifying
x = 7.048664962

Subproblem 2
x + 3.25 = -10.298664962

Simplifying
x + 3.25 = -10.298664962

Reorder the terms:
3.25 + x = -10.298664962

Solving
3.25 + x = -10.298664962

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 = -10.298664962 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -10.298664962 + -3.25
x = -10.298664962 + -3.25

Combine like terms: -10.298664962 + -3.25 = -13.548664962
x = -13.548664962

Simplifying
x = -13.548664962

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.048664962, -13.548664962}