(5p^2)-13p+2=0

Solution for (5p^2)-13p+2=0 equation:

Simplifying
(5p2) + -13p + 2 = 0

Reorder the terms:
2 + -13p + (5p2) = 0

Solving
2 + -13p + (5p2) = 0

Solving for variable 'p'.

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

Divide each side by '5'.
0.4 + -2.6p + p2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.6p + -0.4 + p2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.6p + p2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.6p + p2 = 0 + -0.4
-2.6p + p2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.6p + p2 = -0.4

The p term is -2.6p.  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.
-2.6p + 1.69 + p2 = -0.4 + 1.69

Reorder the terms:
1.69 + -2.6p + p2 = -0.4 + 1.69

Combine like terms: -0.4 + 1.69 = 1.29
1.69 + -2.6p + p2 = 1.29

Factor a perfect square on the left side:
((p) + -1.3)((p) + -1.3) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
((p) + -1.3) equal to 1.135781669 and -1.135781669.

Subproblem 1
(p) + -1.3 = 1.135781669

Simplifying
(p) + -1.3 = 1.135781669
p + -1.3 = 1.135781669

Reorder the terms:
-1.3 + p = 1.135781669

Solving
-1.3 + p = 1.135781669

Solving for variable 'p'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + p = 1.135781669 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + p = 1.135781669 + 1.3
p = 1.135781669 + 1.3

Combine like terms: 1.135781669 + 1.3 = 2.435781669
p = 2.435781669

Simplifying
p = 2.435781669

Subproblem 2
(p) + -1.3 = -1.135781669

Simplifying
(p) + -1.3 = -1.135781669
p + -1.3 = -1.135781669

Reorder the terms:
-1.3 + p = -1.135781669

Solving
-1.3 + p = -1.135781669

Solving for variable 'p'.

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

Add '1.3' to each side of the equation.
-1.3 + 1.3 + p = -1.135781669 + 1.3

Combine like terms: -1.3 + 1.3 = 0.0
0.0 + p = -1.135781669 + 1.3
p = -1.135781669 + 1.3

Combine like terms: -1.135781669 + 1.3 = 0.164218331
p = 0.164218331

Simplifying
p = 0.164218331

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2.435781669, 0.164218331}