2x^2+19x+13=0

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Solution for 2x^2+19x+13=0 equation: 


Simplifying
2x2 + 19x + 13 = 0

Reorder the terms:
13 + 19x + 2x2 = 0

Solving
13 + 19x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
6.5 + 9.5x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 9.5x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 9.5x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 9.5x + x2 = 0 + -6.5
9.5x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
9.5x + x2 = -6.5

The x term is 9.5x.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5x + 22.5625 + x2 = -6.5 + 22.5625

Reorder the terms:
22.5625 + 9.5x + x2 = -6.5 + 22.5625

Combine like terms: -6.5 + 22.5625 = 16.0625
22.5625 + 9.5x + x2 = 16.0625

Factor a perfect square on the left side:
(x + 4.75)(x + 4.75) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(x + 4.75) equal to 4.007804885 and -4.007804885.


Subproblem 1
x + 4.75 = 4.007804885

Simplifying
x + 4.75 = 4.007804885

Reorder the terms:
4.75 + x = 4.007804885

Solving
4.75 + x = 4.007804885

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = 4.007804885 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = 4.007804885 + -4.75
x = 4.007804885 + -4.75

Combine like terms: 4.007804885 + -4.75 = -0.742195115
x = -0.742195115

Simplifying
x = -0.742195115


Subproblem 2
x + 4.75 = -4.007804885

Simplifying
x + 4.75 = -4.007804885

Reorder the terms:
4.75 + x = -4.007804885

Solving
4.75 + x = -4.007804885

Solving for variable 'x'.

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

Add '-4.75' to each side of the equation.
4.75 + -4.75 + x = -4.007804885 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + x = -4.007804885 + -4.75
x = -4.007804885 + -4.75

Combine like terms: -4.007804885 + -4.75 = -8.757804885
x = -8.757804885

Simplifying
x = -8.757804885


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.742195115, -8.757804885}

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