2b^2+4b=2

Solution for 2b^2+4b=2 equation:

Simplifying
2b2 + 4b = 2

Reorder the terms:
4b + 2b2 = 2

Solving
4b + 2b2 = 2

Solving for variable 'b'.

Reorder the terms:
-2 + 4b + 2b2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 4b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2b + b2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + 2b + b2)' equal to zero and attempt to solve:

Simplifying
-1 + 2b + b2 = 0

Solving
-1 + 2b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2b + 1 + b2 = 0 + 1

Reorder the terms:
-1 + 1 + 2b + b2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2b + b2 = 0 + 1
2b + b2 = 0 + 1

Combine like terms: 0 + 1 = 1
2b + b2 = 1

The b term is 2b.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2b + 1 + b2 = 1 + 1

Reorder the terms:
1 + 2b + b2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2b + b2 = 2

Factor a perfect square on the left side:
(b + 1)(b + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(b + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
b + 1 = 1.414213562

Simplifying
b + 1 = 1.414213562

Reorder the terms:
1 + b = 1.414213562

Solving
1 + b = 1.414213562

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + b = 1.414213562 + -1
b = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
b = 0.414213562

Simplifying
b = 0.414213562

Subproblem 2
b + 1 = -1.414213562

Simplifying
b + 1 = -1.414213562

Reorder the terms:
1 + b = -1.414213562

Solving
1 + b = -1.414213562

Solving for variable 'b'.

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

Add '-1' to each side of the equation.
1 + -1 + b = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + b = -1.414213562 + -1
b = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
b = -2.414213562

Simplifying
b = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.414213562, -2.414213562}
Solution
b = {0.414213562, -2.414213562}