3b+6=b^2+4

Solution for 3b+6=b^2+4 equation:

Simplifying
3b + 6 = b2 + 4

Reorder the terms:
6 + 3b = b2 + 4

Reorder the terms:
6 + 3b = 4 + b2

Solving
6 + 3b = 4 + b2

Solving for variable 'b'.

Reorder the terms:
6 + -4 + 3b + -1b2 = 4 + b2 + -4 + -1b2

Combine like terms: 6 + -4 = 2
2 + 3b + -1b2 = 4 + b2 + -4 + -1b2

Reorder the terms:
2 + 3b + -1b2 = 4 + -4 + b2 + -1b2

Combine like terms: 4 + -4 = 0
2 + 3b + -1b2 = 0 + b2 + -1b2
2 + 3b + -1b2 = b2 + -1b2

Combine like terms: b2 + -1b2 = 0
2 + 3b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + -3b + b2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3b + 2 + b2 = 0 + 2

Reorder the terms:
-2 + 2 + -3b + b2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3b + b2 = 0 + 2
-3b + b2 = 0 + 2

Combine like terms: 0 + 2 = 2
-3b + b2 = 2

The b term is -3b.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3b + 2.25 + b2 = 2 + 2.25

Reorder the terms:
2.25 + -3b + b2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3b + b2 = 4.25

Factor a perfect square on the left side:
(b + -1.5)(b + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(b + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
b + -1.5 = 2.061552813

Simplifying
b + -1.5 = 2.061552813

Reorder the terms:
-1.5 + b = 2.061552813

Solving
-1.5 + b = 2.061552813

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = 2.061552813 + 1.5
b = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
b = 3.561552813

Simplifying
b = 3.561552813

Subproblem 2
b + -1.5 = -2.061552813

Simplifying
b + -1.5 = -2.061552813

Reorder the terms:
-1.5 + b = -2.061552813

Solving
-1.5 + b = -2.061552813

Solving for variable 'b'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + b = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + b = -2.061552813 + 1.5
b = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
b = -0.561552813

Simplifying
b = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {3.561552813, -0.561552813}