5x^2+26x+1=

Solution for 5x^2+26x+1= equation:

Simplifying
5x2 + 26x + 1 = 0

Reorder the terms:
1 + 26x + 5x2 = 0

Solving
1 + 26x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
0.2 + 5.2x + x2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 5.2x + -0.2 + x2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 5.2x + x2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 5.2x + x2 = 0 + -0.2
5.2x + x2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
5.2x + x2 = -0.2

The x term is 5.2x.  Take half its coefficient (2.6).
Square it (6.76) and add it to both sides.

Add '6.76' to each side of the equation.
5.2x + 6.76 + x2 = -0.2 + 6.76

Reorder the terms:
6.76 + 5.2x + x2 = -0.2 + 6.76

Combine like terms: -0.2 + 6.76 = 6.56
6.76 + 5.2x + x2 = 6.56

Factor a perfect square on the left side:
(x + 2.6)(x + 2.6) = 6.56

Calculate the square root of the right side: 2.561249695

Break this problem into two subproblems by setting 
(x + 2.6) equal to 2.561249695 and -2.561249695.

Subproblem 1
x + 2.6 = 2.561249695

Simplifying
x + 2.6 = 2.561249695

Reorder the terms:
2.6 + x = 2.561249695

Solving
2.6 + x = 2.561249695

Solving for variable 'x'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + x = 2.561249695 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + x = 2.561249695 + -2.6
x = 2.561249695 + -2.6

Combine like terms: 2.561249695 + -2.6 = -0.038750305
x = -0.038750305

Simplifying
x = -0.038750305

Subproblem 2
x + 2.6 = -2.561249695

Simplifying
x + 2.6 = -2.561249695

Reorder the terms:
2.6 + x = -2.561249695

Solving
2.6 + x = -2.561249695

Solving for variable 'x'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + x = -2.561249695 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + x = -2.561249695 + -2.6
x = -2.561249695 + -2.6

Combine like terms: -2.561249695 + -2.6 = -5.161249695
x = -5.161249695

Simplifying
x = -5.161249695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.038750305, -5.161249695}