0.25p^2+2p=-3

Solution for 0.25p^2+2p=-3 equation:

Simplifying
0.25p2 + 2p = -3

Reorder the terms:
2p + 0.25p2 = -3

Solving
2p + 0.25p2 = -3

Solving for variable 'p'.

Reorder the terms:
3 + 2p + 0.25p2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 2p + 0.25p2 = 0

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

Divide each side by '0.25'.
12 + 8p + p2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 8p + -12 + p2 = 0 + -12

Reorder the terms:
12 + -12 + 8p + p2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 8p + p2 = 0 + -12
8p + p2 = 0 + -12

Combine like terms: 0 + -12 = -12
8p + p2 = -12

The p term is 8p.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8p + 16 + p2 = -12 + 16

Reorder the terms:
16 + 8p + p2 = -12 + 16

Combine like terms: -12 + 16 = 4
16 + 8p + p2 = 4

Factor a perfect square on the left side:
(p + 4)(p + 4) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(p + 4) equal to 2 and -2.

Subproblem 1
p + 4 = 2

Simplifying
p + 4 = 2

Reorder the terms:
4 + p = 2

Solving
4 + p = 2

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = 2 + -4

Combine like terms: 4 + -4 = 0
0 + p = 2 + -4
p = 2 + -4

Combine like terms: 2 + -4 = -2
p = -2

Simplifying
p = -2

Subproblem 2
p + 4 = -2

Simplifying
p + 4 = -2

Reorder the terms:
4 + p = -2

Solving
4 + p = -2

Solving for variable 'p'.

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

Add '-4' to each side of the equation.
4 + -4 + p = -2 + -4

Combine like terms: 4 + -4 = 0
0 + p = -2 + -4
p = -2 + -4

Combine like terms: -2 + -4 = -6
p = -6

Simplifying
p = -6

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-2, -6}