4b^2+45b+40=0

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Solution for 4b^2+45b+40=0 equation: 


Simplifying
4b2 + 45b + 40 = 0

Reorder the terms:
40 + 45b + 4b2 = 0

Solving
40 + 45b + 4b2 = 0

Solving for variable 'b'.

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

Divide each side by '4'.
10 + 11.25b + b2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 11.25b + -10 + b2 = 0 + -10

Reorder the terms:
10 + -10 + 11.25b + b2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 11.25b + b2 = 0 + -10
11.25b + b2 = 0 + -10

Combine like terms: 0 + -10 = -10
11.25b + b2 = -10

The b term is 11.25b.  Take half its coefficient (5.625).
Square it (31.640625) and add it to both sides.

Add '31.640625' to each side of the equation.
11.25b + 31.640625 + b2 = -10 + 31.640625

Reorder the terms:
31.640625 + 11.25b + b2 = -10 + 31.640625

Combine like terms: -10 + 31.640625 = 21.640625
31.640625 + 11.25b + b2 = 21.640625

Factor a perfect square on the left side:
(b + 5.625)(b + 5.625) = 21.640625

Calculate the square root of the right side: 4.651948516

Break this problem into two subproblems by setting 
(b + 5.625) equal to 4.651948516 and -4.651948516.


Subproblem 1
b + 5.625 = 4.651948516

Simplifying
b + 5.625 = 4.651948516

Reorder the terms:
5.625 + b = 4.651948516

Solving
5.625 + b = 4.651948516

Solving for variable 'b'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + b = 4.651948516 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + b = 4.651948516 + -5.625
b = 4.651948516 + -5.625

Combine like terms: 4.651948516 + -5.625 = -0.973051484
b = -0.973051484

Simplifying
b = -0.973051484


Subproblem 2
b + 5.625 = -4.651948516

Simplifying
b + 5.625 = -4.651948516

Reorder the terms:
5.625 + b = -4.651948516

Solving
5.625 + b = -4.651948516

Solving for variable 'b'.

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

Add '-5.625' to each side of the equation.
5.625 + -5.625 + b = -4.651948516 + -5.625

Combine like terms: 5.625 + -5.625 = 0.000
0.000 + b = -4.651948516 + -5.625
b = -4.651948516 + -5.625

Combine like terms: -4.651948516 + -5.625 = -10.276948516
b = -10.276948516

Simplifying
b = -10.276948516


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.973051484, -10.276948516}

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