p-1*5p+2=4p^2

Solution for p-1*5p+2=4p^2 equation:

Simplifying
p + -1 * 5p + 2 = 4p2

Multiply -1 * 5
p + -5p + 2 = 4p2

Reorder the terms:
2 + p + -5p = 4p2

Combine like terms: p + -5p = -4p
2 + -4p = 4p2

Solving
2 + -4p = 4p2

Solving for variable 'p'.

Combine like terms: 4p2 + -4p2 = 0
2 + -4p + -4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2p + -2p2) = 0

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

Simplifying
1 + -2p + -2p2 = 0

Solving
1 + -2p + -2p2 = 0

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

Divide each side by '-2'.
-0.5 + p + p2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + p + 0.5 + p2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + p + p2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + p + p2 = 0 + 0.5
p + p2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
p + p2 = 0.5

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + p2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + p2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + p2 = 0.75

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(p + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
p + 0.5 = 0.866025404

Simplifying
p + 0.5 = 0.866025404

Reorder the terms:
0.5 + p = 0.866025404

Solving
0.5 + p = 0.866025404

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 0.866025404 + -0.5
p = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
p = 0.366025404

Simplifying
p = 0.366025404

Subproblem 2
p + 0.5 = -0.866025404

Simplifying
p + 0.5 = -0.866025404

Reorder the terms:
0.5 + p = -0.866025404

Solving
0.5 + p = -0.866025404

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -0.866025404 + -0.5
p = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
p = -1.366025404

Simplifying
p = -1.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.366025404, -1.366025404}
Solution
p = {0.366025404, -1.366025404}