2p^2+5p-8=0

Solution for 2p^2+5p-8=0 equation:

Simplifying
2p2 + 5p + -8 = 0

Reorder the terms:
-8 + 5p + 2p2 = 0

Solving
-8 + 5p + 2p2 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
-4 + 2.5p + p2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2.5p + 4 + p2 = 0 + 4

Reorder the terms:
-4 + 4 + 2.5p + p2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2.5p + p2 = 0 + 4
2.5p + p2 = 0 + 4

Combine like terms: 0 + 4 = 4
2.5p + p2 = 4

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 = 4 + 1.5625

Reorder the terms:
1.5625 + 2.5p + p2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + 2.5p + p2 = 5.5625

Factor a perfect square on the left side:
(p + 1.25)(p + 1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(p + 1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
p + 1.25 = 2.358495283

Simplifying
p + 1.25 = 2.358495283

Reorder the terms:
1.25 + p = 2.358495283

Solving
1.25 + p = 2.358495283

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 = 2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + p = 2.358495283 + -1.25
p = 2.358495283 + -1.25

Combine like terms: 2.358495283 + -1.25 = 1.108495283
p = 1.108495283

Simplifying
p = 1.108495283

Subproblem 2
p + 1.25 = -2.358495283

Simplifying
p + 1.25 = -2.358495283

Reorder the terms:
1.25 + p = -2.358495283

Solving
1.25 + p = -2.358495283

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 = -2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + p = -2.358495283 + -1.25
p = -2.358495283 + -1.25

Combine like terms: -2.358495283 + -1.25 = -3.608495283
p = -3.608495283

Simplifying
p = -3.608495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.108495283, -3.608495283}