10x^2+26x+6=0

Solution for 10x^2+26x+6=0 equation:

Simplifying
10x2 + 26x + 6 = 0

Reorder the terms:
6 + 26x + 10x2 = 0

Solving
6 + 26x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 13x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 13x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + 13x + 5x2 = 0

Solving
3 + 13x + 5x2 = 0

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

Divide each side by '5'.
0.6 + 2.6x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2.6x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2.6x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2.6x + x2 = 0 + -0.6
2.6x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
2.6x + x2 = -0.6

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = -0.6 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = -0.6 + 1.69

Combine like terms: -0.6 + 1.69 = 1.09
1.69 + 2.6x + x2 = 1.09

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 1.09

Calculate the square root of the right side: 1.044030651

Break this problem into two subproblems by setting 
(x + 1.3) equal to 1.044030651 and -1.044030651.

Subproblem 1
x + 1.3 = 1.044030651

Simplifying
x + 1.3 = 1.044030651

Reorder the terms:
1.3 + x = 1.044030651

Solving
1.3 + x = 1.044030651

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = 1.044030651 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = 1.044030651 + -1.3
x = 1.044030651 + -1.3

Combine like terms: 1.044030651 + -1.3 = -0.255969349
x = -0.255969349

Simplifying
x = -0.255969349

Subproblem 2
x + 1.3 = -1.044030651

Simplifying
x + 1.3 = -1.044030651

Reorder the terms:
1.3 + x = -1.044030651

Solving
1.3 + x = -1.044030651

Solving for variable 'x'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + x = -1.044030651 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + x = -1.044030651 + -1.3
x = -1.044030651 + -1.3

Combine like terms: -1.044030651 + -1.3 = -2.344030651
x = -2.344030651

Simplifying
x = -2.344030651

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.255969349, -2.344030651}
Solution
x = {-0.255969349, -2.344030651}