b^2-16b+40=0

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Solution for b^2-16b+40=0 equation: 


Simplifying
b2 + -16b + 40 = 0

Reorder the terms:
40 + -16b + b2 = 0

Solving
40 + -16b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -16b + -40 + b2 = 0 + -40

Reorder the terms:
40 + -40 + -16b + b2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -16b + b2 = 0 + -40
-16b + b2 = 0 + -40

Combine like terms: 0 + -40 = -40
-16b + b2 = -40

The b term is -16b.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16b + 64 + b2 = -40 + 64

Reorder the terms:
64 + -16b + b2 = -40 + 64

Combine like terms: -40 + 64 = 24
64 + -16b + b2 = 24

Factor a perfect square on the left side:
(b + -8)(b + -8) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(b + -8) equal to 4.898979486 and -4.898979486.


Subproblem 1
b + -8 = 4.898979486

Simplifying
b + -8 = 4.898979486

Reorder the terms:
-8 + b = 4.898979486

Solving
-8 + b = 4.898979486

Solving for variable 'b'.

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

Add '8' to each side of the equation.
-8 + 8 + b = 4.898979486 + 8

Combine like terms: -8 + 8 = 0
0 + b = 4.898979486 + 8
b = 4.898979486 + 8

Combine like terms: 4.898979486 + 8 = 12.898979486
b = 12.898979486

Simplifying
b = 12.898979486


Subproblem 2
b + -8 = -4.898979486

Simplifying
b + -8 = -4.898979486

Reorder the terms:
-8 + b = -4.898979486

Solving
-8 + b = -4.898979486

Solving for variable 'b'.

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

Add '8' to each side of the equation.
-8 + 8 + b = -4.898979486 + 8

Combine like terms: -8 + 8 = 0
0 + b = -4.898979486 + 8
b = -4.898979486 + 8

Combine like terms: -4.898979486 + 8 = 3.101020514
b = 3.101020514

Simplifying
b = 3.101020514


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {12.898979486, 3.101020514}

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