7r^2+6r+1=0

Solution for 7r^2+6r+1=0 equation:

Simplifying
7r2 + 6r + 1 = 0

Reorder the terms:
1 + 6r + 7r2 = 0

Solving
1 + 6r + 7r2 = 0

Solving for variable 'r'.

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

Divide each side by '7'.
0.1428571429 + 0.8571428571r + r2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + 0.8571428571r + -0.1428571429 + r2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + 0.8571428571r + r2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + 0.8571428571r + r2 = 0 + -0.1428571429
0.8571428571r + r2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
0.8571428571r + r2 = -0.1428571429

The r term is 0.8571428571r.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571r + 0.1836734694 + r2 = -0.1428571429 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571r + r2 = -0.1428571429 + 0.1836734694

Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265
0.1836734694 + 0.8571428571r + r2 = 0.0408163265

Factor a perfect square on the left side:
(r + 0.4285714286)(r + 0.4285714286) = 0.0408163265

Calculate the square root of the right side: 0.202030509

Break this problem into two subproblems by setting 
(r + 0.4285714286) equal to 0.202030509 and -0.202030509.

Subproblem 1
r + 0.4285714286 = 0.202030509

Simplifying
r + 0.4285714286 = 0.202030509

Reorder the terms:
0.4285714286 + r = 0.202030509

Solving
0.4285714286 + r = 0.202030509

Solving for variable 'r'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + r = 0.202030509 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + r = 0.202030509 + -0.4285714286
r = 0.202030509 + -0.4285714286

Combine like terms: 0.202030509 + -0.4285714286 = -0.2265409196
r = -0.2265409196

Simplifying
r = -0.2265409196

Subproblem 2
r + 0.4285714286 = -0.202030509

Simplifying
r + 0.4285714286 = -0.202030509

Reorder the terms:
0.4285714286 + r = -0.202030509

Solving
0.4285714286 + r = -0.202030509

Solving for variable 'r'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + r = -0.202030509 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + r = -0.202030509 + -0.4285714286
r = -0.202030509 + -0.4285714286

Combine like terms: -0.202030509 + -0.4285714286 = -0.6306019376
r = -0.6306019376

Simplifying
r = -0.6306019376

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.2265409196, -0.6306019376}