7p^2-6p+1=0

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

Simplifying
7p2 + -6p + 1 = 0

Reorder the terms:
1 + -6p + 7p2 = 0

Solving
1 + -6p + 7p2 = 0

Solving for variable 'p'.

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

Divide each side by '7'.
0.1428571429 + -0.8571428571p + p2 = 0

Move the constant term to the right:

Add '-0.1428571429' to each side of the equation.
0.1428571429 + -0.8571428571p + -0.1428571429 + p2 = 0 + -0.1428571429

Reorder the terms:
0.1428571429 + -0.1428571429 + -0.8571428571p + p2 = 0 + -0.1428571429

Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000
0.0000000000 + -0.8571428571p + p2 = 0 + -0.1428571429
-0.8571428571p + p2 = 0 + -0.1428571429

Combine like terms: 0 + -0.1428571429 = -0.1428571429
-0.8571428571p + p2 = -0.1428571429

The p term is -0.8571428571p.  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.
-0.8571428571p + 0.1836734694 + p2 = -0.1428571429 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571p + p2 = -0.1428571429 + 0.1836734694

Combine like terms: -0.1428571429 + 0.1836734694 = 0.0408163265
0.1836734694 + -0.8571428571p + p2 = 0.0408163265

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

Calculate the square root of the right side: 0.202030509

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

Subproblem 1
p + -0.4285714286 = 0.202030509

Simplifying
p + -0.4285714286 = 0.202030509

Reorder the terms:
-0.4285714286 + p = 0.202030509

Solving
-0.4285714286 + p = 0.202030509

Solving for variable 'p'.

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

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

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

Combine like terms: 0.202030509 + 0.4285714286 = 0.6306019376
p = 0.6306019376

Simplifying
p = 0.6306019376

Subproblem 2
p + -0.4285714286 = -0.202030509

Simplifying
p + -0.4285714286 = -0.202030509

Reorder the terms:
-0.4285714286 + p = -0.202030509

Solving
-0.4285714286 + p = -0.202030509

Solving for variable 'p'.

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

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

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

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

Simplifying
p = 0.2265409196

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