5p^2=-26p+5

Solution for 5p^2=-26p+5 equation:

Simplifying
5p2 = -26p + 5

Reorder the terms:
5p2 = 5 + -26p

Solving
5p2 = 5 + -26p

Solving for variable 'p'.

Reorder the terms:
-5 + 26p + 5p2 = 5 + -26p + -5 + 26p

Reorder the terms:
-5 + 26p + 5p2 = 5 + -5 + -26p + 26p

Combine like terms: 5 + -5 = 0
-5 + 26p + 5p2 = 0 + -26p + 26p
-5 + 26p + 5p2 = -26p + 26p

Combine like terms: -26p + 26p = 0
-5 + 26p + 5p2 = 0

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

Divide each side by '5'.
-1 + 5.2p + p2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 5.2p + 1 + p2 = 0 + 1

Reorder the terms:
-1 + 1 + 5.2p + p2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5.2p + p2 = 0 + 1
5.2p + p2 = 0 + 1

Combine like terms: 0 + 1 = 1
5.2p + p2 = 1

The p term is 5.2p.  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.
5.2p + 6.76 + p2 = 1 + 6.76

Reorder the terms:
6.76 + 5.2p + p2 = 1 + 6.76

Combine like terms: 1 + 6.76 = 7.76
6.76 + 5.2p + p2 = 7.76

Factor a perfect square on the left side:
(p + 2.6)(p + 2.6) = 7.76

Calculate the square root of the right side: 2.785677655

Break this problem into two subproblems by setting 
(p + 2.6) equal to 2.785677655 and -2.785677655.

Subproblem 1
p + 2.6 = 2.785677655

Simplifying
p + 2.6 = 2.785677655

Reorder the terms:
2.6 + p = 2.785677655

Solving
2.6 + p = 2.785677655

Solving for variable 'p'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + p = 2.785677655 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + p = 2.785677655 + -2.6
p = 2.785677655 + -2.6

Combine like terms: 2.785677655 + -2.6 = 0.185677655
p = 0.185677655

Simplifying
p = 0.185677655

Subproblem 2
p + 2.6 = -2.785677655

Simplifying
p + 2.6 = -2.785677655

Reorder the terms:
2.6 + p = -2.785677655

Solving
2.6 + p = -2.785677655

Solving for variable 'p'.

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

Add '-2.6' to each side of the equation.
2.6 + -2.6 + p = -2.785677655 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + p = -2.785677655 + -2.6
p = -2.785677655 + -2.6

Combine like terms: -2.785677655 + -2.6 = -5.385677655
p = -5.385677655

Simplifying
p = -5.385677655

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.185677655, -5.385677655}