18p^4-4p^2-20=0

Solution for 18p^4-4p^2-20=0 equation:

Simplifying
18p4 + -4p2 + -20 = 0

Reorder the terms:
-20 + -4p2 + 18p4 = 0

Solving
-20 + -4p2 + 18p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -2p2 + 9p4) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -2p2 + 9p4)' equal to zero and attempt to solve:

Simplifying
-10 + -2p2 + 9p4 = 0

Solving
-10 + -2p2 + 9p4 = 0

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

Divide each side by '9'.
-1.111111111 + -0.2222222222p2 + p4 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -0.2222222222p2 + 1.111111111 + p4 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -0.2222222222p2 + p4 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -0.2222222222p2 + p4 = 0 + 1.111111111
-0.2222222222p2 + p4 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-0.2222222222p2 + p4 = 1.111111111

The p term is -0.2222222222p2.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222p2 + 0.01234567901 + p4 = 1.111111111 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222p2 + p4 = 1.111111111 + 0.01234567901

Combine like terms: 1.111111111 + 0.01234567901 = 1.12345679001
0.01234567901 + -0.2222222222p2 + p4 = 1.12345679001

Factor a perfect square on the left side:
(p2 + -0.1111111111)(p2 + -0.1111111111) = 1.12345679001

Calculate the square root of the right side: 1.059932446

Break this problem into two subproblems by setting 
(p2 + -0.1111111111) equal to 1.059932446 and -1.059932446.

Subproblem 1
p2 + -0.1111111111 = 1.059932446

Simplifying
p2 + -0.1111111111 = 1.059932446

Reorder the terms:
-0.1111111111 + p2 = 1.059932446

Solving
-0.1111111111 + p2 = 1.059932446

Solving for variable 'p'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + p2 = 1.059932446 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + p2 = 1.059932446 + 0.1111111111
p2 = 1.059932446 + 0.1111111111

Combine like terms: 1.059932446 + 0.1111111111 = 1.1710435571
p2 = 1.1710435571

Simplifying
p2 = 1.1710435571

Take the square root of each side:
p = {-1.08214766, 1.08214766}

Subproblem 2
p2 + -0.1111111111 = -1.059932446

Simplifying
p2 + -0.1111111111 = -1.059932446

Reorder the terms:
-0.1111111111 + p2 = -1.059932446

Solving
-0.1111111111 + p2 = -1.059932446

Solving for variable 'p'.

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

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.1111111111 + p2 = -1.059932446 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + p2 = -1.059932446 + 0.1111111111
p2 = -1.059932446 + 0.1111111111

Combine like terms: -1.059932446 + 0.1111111111 = -0.9488213349
p2 = -0.9488213349

Simplifying
p2 = -0.9488213349

Reorder the terms:
0.9488213349 + p2 = -0.9488213349 + 0.9488213349

Combine like terms: -0.9488213349 + 0.9488213349 = 0.0000000000
0.9488213349 + p2 = 0.0000000000

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.

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

The solution to this equation could not be determined.