2p=p^2+1

Solution for 2p=p^2+1 equation:

Simplifying
2p = p2 + 1

Reorder the terms:
2p = 1 + p2

Solving
2p = 1 + p2

Solving for variable 'p'.

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

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

Combine like terms: 1 + -1 = 0
-1 + 2p + -1p2 = 0 + p2 + -1p2
-1 + 2p + -1p2 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-1 + 2p + -1p2 = 0

Factor a trinomial.
(-1 + p)(1 + -1p) = 0

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

Simplifying
-1 + p = 0

Solving
-1 + p = 0

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 = 0 + 1

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

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

Simplifying
p = 1
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1

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

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

Divide each side by '-1'.
p = 1

Simplifying
p = 1
Solution
p = {1, 1}