4b^2-40b-64=0

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Solution for 4b^2-40b-64=0 equation: 


Simplifying
4b2 + -40b + -64 = 0

Reorder the terms:
-64 + -40b + 4b2 = 0

Solving
-64 + -40b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -10b + b2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -10b + b2)' equal to zero and attempt to solve:

Simplifying
-16 + -10b + b2 = 0

Solving
-16 + -10b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10b + 16 + b2 = 0 + 16

Reorder the terms:
-16 + 16 + -10b + b2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10b + b2 = 0 + 16
-10b + b2 = 0 + 16

Combine like terms: 0 + 16 = 16
-10b + b2 = 16

The b term is -10b.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10b + 25 + b2 = 16 + 25

Reorder the terms:
25 + -10b + b2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10b + b2 = 41

Factor a perfect square on the left side:
(b + -5)(b + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(b + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
b + -5 = 6.403124237

Simplifying
b + -5 = 6.403124237

Reorder the terms:
-5 + b = 6.403124237

Solving
-5 + b = 6.403124237

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + b = 6.403124237 + 5
b = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
b = 11.403124237

Simplifying
b = 11.403124237


Subproblem 2
b + -5 = -6.403124237

Simplifying
b + -5 = -6.403124237

Reorder the terms:
-5 + b = -6.403124237

Solving
-5 + b = -6.403124237

Solving for variable 'b'.

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

Add '5' to each side of the equation.
-5 + 5 + b = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + b = -6.403124237 + 5
b = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
b = -1.403124237

Simplifying
b = -1.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {11.403124237, -1.403124237}
Solution
b = {11.403124237, -1.403124237}

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