b^2+47b+20=0

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Solution for b^2+47b+20=0 equation: 


Simplifying
b2 + 47b + 20 = 0

Reorder the terms:
20 + 47b + b2 = 0

Solving
20 + 47b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 47b + -20 + b2 = 0 + -20

Reorder the terms:
20 + -20 + 47b + b2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 47b + b2 = 0 + -20
47b + b2 = 0 + -20

Combine like terms: 0 + -20 = -20
47b + b2 = -20

The b term is 47b.  Take half its coefficient (23.5).
Square it (552.25) and add it to both sides.

Add '552.25' to each side of the equation.
47b + 552.25 + b2 = -20 + 552.25

Reorder the terms:
552.25 + 47b + b2 = -20 + 552.25

Combine like terms: -20 + 552.25 = 532.25
552.25 + 47b + b2 = 532.25

Factor a perfect square on the left side:
(b + 23.5)(b + 23.5) = 532.25

Calculate the square root of the right side: 23.07054399

Break this problem into two subproblems by setting 
(b + 23.5) equal to 23.07054399 and -23.07054399.


Subproblem 1
b + 23.5 = 23.07054399

Simplifying
b + 23.5 = 23.07054399

Reorder the terms:
23.5 + b = 23.07054399

Solving
23.5 + b = 23.07054399

Solving for variable 'b'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + b = 23.07054399 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + b = 23.07054399 + -23.5
b = 23.07054399 + -23.5

Combine like terms: 23.07054399 + -23.5 = -0.42945601
b = -0.42945601

Simplifying
b = -0.42945601


Subproblem 2
b + 23.5 = -23.07054399

Simplifying
b + 23.5 = -23.07054399

Reorder the terms:
23.5 + b = -23.07054399

Solving
23.5 + b = -23.07054399

Solving for variable 'b'.

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

Add '-23.5' to each side of the equation.
23.5 + -23.5 + b = -23.07054399 + -23.5

Combine like terms: 23.5 + -23.5 = 0.0
0.0 + b = -23.07054399 + -23.5
b = -23.07054399 + -23.5

Combine like terms: -23.07054399 + -23.5 = -46.57054399
b = -46.57054399

Simplifying
b = -46.57054399


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.42945601, -46.57054399}

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