5p^2-11p+4=0

Solution for 5p^2-11p+4=0 equation:

Simplifying
5p2 + -11p + 4 = 0

Reorder the terms:
4 + -11p + 5p2 = 0

Solving
4 + -11p + 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'.
0.8 + -2.2p + p2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.2p + -0.8 + p2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.2p + p2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.2p + p2 = 0 + -0.8
-2.2p + p2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.2p + p2 = -0.8

The p term is -2.2p.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2p + 1.21 + p2 = -0.8 + 1.21

Reorder the terms:
1.21 + -2.2p + p2 = -0.8 + 1.21

Combine like terms: -0.8 + 1.21 = 0.41
1.21 + -2.2p + p2 = 0.41

Factor a perfect square on the left side:
(p + -1.1)(p + -1.1) = 0.41

Calculate the square root of the right side: 0.640312424

Break this problem into two subproblems by setting 
(p + -1.1) equal to 0.640312424 and -0.640312424.

Subproblem 1
p + -1.1 = 0.640312424

Simplifying
p + -1.1 = 0.640312424

Reorder the terms:
-1.1 + p = 0.640312424

Solving
-1.1 + p = 0.640312424

Solving for variable 'p'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + p = 0.640312424 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + p = 0.640312424 + 1.1
p = 0.640312424 + 1.1

Combine like terms: 0.640312424 + 1.1 = 1.740312424
p = 1.740312424

Simplifying
p = 1.740312424

Subproblem 2
p + -1.1 = -0.640312424

Simplifying
p + -1.1 = -0.640312424

Reorder the terms:
-1.1 + p = -0.640312424

Solving
-1.1 + p = -0.640312424

Solving for variable 'p'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + p = -0.640312424 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + p = -0.640312424 + 1.1
p = -0.640312424 + 1.1

Combine like terms: -0.640312424 + 1.1 = 0.459687576
p = 0.459687576

Simplifying
p = 0.459687576

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.740312424, 0.459687576}