4p^2-8p+578=0

Solution for 4p^2-8p+578=0 equation:

Simplifying
4p2 + -8p + 578 = 0

Reorder the terms:
578 + -8p + 4p2 = 0

Solving
578 + -8p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(289 + -4p + 2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(289 + -4p + 2p2)' equal to zero and attempt to solve:

Simplifying
289 + -4p + 2p2 = 0

Solving
289 + -4p + 2p2 = 0

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

Divide each side by '2'.
144.5 + -2p + p2 = 0

Move the constant term to the right:

Add '-144.5' to each side of the equation.
144.5 + -2p + -144.5 + p2 = 0 + -144.5

Reorder the terms:
144.5 + -144.5 + -2p + p2 = 0 + -144.5

Combine like terms: 144.5 + -144.5 = 0.0
0.0 + -2p + p2 = 0 + -144.5
-2p + p2 = 0 + -144.5

Combine like terms: 0 + -144.5 = -144.5
-2p + p2 = -144.5

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 = -144.5 + 1

Reorder the terms:
1 + -2p + p2 = -144.5 + 1

Combine like terms: -144.5 + 1 = -143.5
1 + -2p + p2 = -143.5

Factor a perfect square on the left side:
(p + -1)(p + -1) = -143.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.