0.8p^2-2p=-0.8

Solution for 0.8p^2-2p=-0.8 equation:

Simplifying
0.8p2 + -2p = -0.8

Reorder the terms:
-2p + 0.8p2 = -0.8

Solving
-2p + 0.8p2 = -0.8

Solving for variable 'p'.

Reorder the terms:
0.8 + -2p + 0.8p2 = -0.8 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.8 + -2p + 0.8p2 = 0.0

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

Divide each side by '0.8'.
1 + -2.5p + p2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.5p + -1 + p2 = 0 + -1

Reorder the terms:
1 + -1 + -2.5p + p2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.5p + p2 = 0 + -1
-2.5p + p2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.5p + p2 = -1

The p term is -2.5p.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5p + 1.5625 + p2 = -1 + 1.5625

Reorder the terms:
1.5625 + -2.5p + p2 = -1 + 1.5625

Combine like terms: -1 + 1.5625 = 0.5625
1.5625 + -2.5p + p2 = 0.5625

Factor a perfect square on the left side:
(p + -1.25)(p + -1.25) = 0.5625

Calculate the square root of the right side: 0.75

Break this problem into two subproblems by setting 
(p + -1.25) equal to 0.75 and -0.75.

Subproblem 1
p + -1.25 = 0.75

Simplifying
p + -1.25 = 0.75

Reorder the terms:
-1.25 + p = 0.75

Solving
-1.25 + p = 0.75

Solving for variable 'p'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + p = 0.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + p = 0.75 + 1.25
p = 0.75 + 1.25

Combine like terms: 0.75 + 1.25 = 2
p = 2

Simplifying
p = 2

Subproblem 2
p + -1.25 = -0.75

Simplifying
p + -1.25 = -0.75

Reorder the terms:
-1.25 + p = -0.75

Solving
-1.25 + p = -0.75

Solving for variable 'p'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + p = -0.75 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + p = -0.75 + 1.25
p = -0.75 + 1.25

Combine like terms: -0.75 + 1.25 = 0.5
p = 0.5

Simplifying
p = 0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {2, 0.5}