-2b^2+4b+3=4

Solution for -2b^2+4b+3=4 equation:

Simplifying
-2b2 + 4b + 3 = 4

Reorder the terms:
3 + 4b + -2b2 = 4

Solving
3 + 4b + -2b2 = 4

Solving for variable 'b'.

Reorder the terms:
3 + -4 + 4b + -2b2 = 4 + -4

Combine like terms: 3 + -4 = -1
-1 + 4b + -2b2 = 4 + -4

Combine like terms: 4 + -4 = 0
-1 + 4b + -2b2 = 0

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

Divide each side by '-2'.
0.5 + -2b + b2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -2b + -0.5 + b2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -2b + b2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -2b + b2 = 0 + -0.5
-2b + b2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-2b + b2 = -0.5

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 = -0.5 + 1

Reorder the terms:
1 + -2b + b2 = -0.5 + 1

Combine like terms: -0.5 + 1 = 0.5
1 + -2b + b2 = 0.5

Factor a perfect square on the left side:
(b + -1)(b + -1) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(b + -1) equal to 0.707106781 and -0.707106781.

Subproblem 1
b + -1 = 0.707106781

Simplifying
b + -1 = 0.707106781

Reorder the terms:
-1 + b = 0.707106781

Solving
-1 + b = 0.707106781

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 = 0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + b = 0.707106781 + 1
b = 0.707106781 + 1

Combine like terms: 0.707106781 + 1 = 1.707106781
b = 1.707106781

Simplifying
b = 1.707106781

Subproblem 2
b + -1 = -0.707106781

Simplifying
b + -1 = -0.707106781

Reorder the terms:
-1 + b = -0.707106781

Solving
-1 + b = -0.707106781

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 = -0.707106781 + 1

Combine like terms: -1 + 1 = 0
0 + b = -0.707106781 + 1
b = -0.707106781 + 1

Combine like terms: -0.707106781 + 1 = 0.292893219
b = 0.292893219

Simplifying
b = 0.292893219

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.707106781, 0.292893219}