w=2w^2+1

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

Simplifying
w = 2w2 + 1

Reorder the terms:
w = 1 + 2w2

Solving
w = 1 + 2w2

Solving for variable 'w'.

Reorder the terms:
-1 + w + -2w2 = 1 + 2w2 + -1 + -2w2

Reorder the terms:
-1 + w + -2w2 = 1 + -1 + 2w2 + -2w2

Combine like terms: 1 + -1 = 0
-1 + w + -2w2 = 0 + 2w2 + -2w2
-1 + w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-1 + w + -2w2 = 0

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

Divide each side by '-2'.
0.5 + -0.5w + w2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -0.5w + -0.5 + w2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -0.5w + w2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -0.5w + w2 = 0 + -0.5
-0.5w + w2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-0.5w + w2 = -0.5

The w term is w.  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.
-0.5w + 0.25 + w2 = -0.5 + 0.25

Reorder the terms:
0.25 + -0.5w + w2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + -0.5w + w2 = -0.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.