b^2-4b-44=0

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Solution for b^2-4b-44=0 equation: 


Simplifying
b2 + -4b + -44 = 0

Reorder the terms:
-44 + -4b + b2 = 0

Solving
-44 + -4b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -4b + 44 + b2 = 0 + 44

Reorder the terms:
-44 + 44 + -4b + b2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -4b + b2 = 0 + 44
-4b + b2 = 0 + 44

Combine like terms: 0 + 44 = 44
-4b + b2 = 44

The b term is -4b.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4b + 4 + b2 = 44 + 4

Reorder the terms:
4 + -4b + b2 = 44 + 4

Combine like terms: 44 + 4 = 48
4 + -4b + b2 = 48

Factor a perfect square on the left side:
(b + -2)(b + -2) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(b + -2) equal to 6.92820323 and -6.92820323.


Subproblem 1
b + -2 = 6.92820323

Simplifying
b + -2 = 6.92820323

Reorder the terms:
-2 + b = 6.92820323

Solving
-2 + b = 6.92820323

Solving for variable 'b'.

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

Add '2' to each side of the equation.
-2 + 2 + b = 6.92820323 + 2

Combine like terms: -2 + 2 = 0
0 + b = 6.92820323 + 2
b = 6.92820323 + 2

Combine like terms: 6.92820323 + 2 = 8.92820323
b = 8.92820323

Simplifying
b = 8.92820323


Subproblem 2
b + -2 = -6.92820323

Simplifying
b + -2 = -6.92820323

Reorder the terms:
-2 + b = -6.92820323

Solving
-2 + b = -6.92820323

Solving for variable 'b'.

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

Add '2' to each side of the equation.
-2 + 2 + b = -6.92820323 + 2

Combine like terms: -2 + 2 = 0
0 + b = -6.92820323 + 2
b = -6.92820323 + 2

Combine like terms: -6.92820323 + 2 = -4.92820323
b = -4.92820323

Simplifying
b = -4.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {8.92820323, -4.92820323}

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