8p^2-16p-34=0

Solution for 8p^2-16p-34=0 equation:

Simplifying
8p2 + -16p + -34 = 0

Reorder the terms:
-34 + -16p + 8p2 = 0

Solving
-34 + -16p + 8p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -8p + 4p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -8p + 4p2)' equal to zero and attempt to solve:

Simplifying
-17 + -8p + 4p2 = 0

Solving
-17 + -8p + 4p2 = 0

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

Divide each side by '4'.
-4.25 + -2p + p2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -2p + 4.25 + p2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -2p + p2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -2p + p2 = 0 + 4.25
-2p + p2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-2p + p2 = 4.25

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 4.25 + 1

Reorder the terms:
1 + -2p + p2 = 4.25 + 1

Combine like terms: 4.25 + 1 = 5.25
1 + -2p + p2 = 5.25

Factor a perfect square on the left side:
(p + -1)(p + -1) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(p + -1) equal to 2.291287847 and -2.291287847.

Subproblem 1
p + -1 = 2.291287847

Simplifying
p + -1 = 2.291287847

Reorder the terms:
-1 + p = 2.291287847

Solving
-1 + p = 2.291287847

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = 2.291287847 + 1

Combine like terms: -1 + 1 = 0
0 + p = 2.291287847 + 1
p = 2.291287847 + 1

Combine like terms: 2.291287847 + 1 = 3.291287847
p = 3.291287847

Simplifying
p = 3.291287847

Subproblem 2
p + -1 = -2.291287847

Simplifying
p + -1 = -2.291287847

Reorder the terms:
-1 + p = -2.291287847

Solving
-1 + p = -2.291287847

Solving for variable 'p'.

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

Add '1' to each side of the equation.
-1 + 1 + p = -2.291287847 + 1

Combine like terms: -1 + 1 = 0
0 + p = -2.291287847 + 1
p = -2.291287847 + 1

Combine like terms: -2.291287847 + 1 = -1.291287847
p = -1.291287847

Simplifying
p = -1.291287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {3.291287847, -1.291287847}
Solution
p = {3.291287847, -1.291287847}