v^2+1=v

Solution for v^2+1=v equation:

Simplifying
v2 + 1 = v

Reorder the terms:
1 + v2 = v

Solving
1 + v2 = v

Solving for variable 'v'.

Reorder the terms:
1 + -1v + v2 = v + -1v

Combine like terms: v + -1v = 0
1 + -1v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1v + -1 + v2 = 0 + -1

Reorder the terms:
1 + -1 + -1v + v2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1v + v2 = 0 + -1
-1v + v2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1v + v2 = -1

The v term is -1v.  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.
-1v + 0.25 + v2 = -1 + 0.25

Reorder the terms:
0.25 + -1v + v2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1v + v2 = -0.75

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.