4b^2-72b+160=0

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Solution for 4b^2-72b+160=0 equation: 


Simplifying
4b2 + -72b + 160 = 0

Reorder the terms:
160 + -72b + 4b2 = 0

Solving
160 + -72b + 4b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + -18b + b2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(40 + -18b + b2)' equal to zero and attempt to solve:

Simplifying
40 + -18b + b2 = 0

Solving
40 + -18b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -18b + -40 + b2 = 0 + -40

Reorder the terms:
40 + -40 + -18b + b2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -18b + b2 = 0 + -40
-18b + b2 = 0 + -40

Combine like terms: 0 + -40 = -40
-18b + b2 = -40

The b term is -18b.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18b + 81 + b2 = -40 + 81

Reorder the terms:
81 + -18b + b2 = -40 + 81

Combine like terms: -40 + 81 = 41
81 + -18b + b2 = 41

Factor a perfect square on the left side:
(b + -9)(b + -9) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(b + -9) equal to 6.403124237 and -6.403124237.


Subproblem 1
b + -9 = 6.403124237

Simplifying
b + -9 = 6.403124237

Reorder the terms:
-9 + b = 6.403124237

Solving
-9 + b = 6.403124237

Solving for variable 'b'.

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

Add '9' to each side of the equation.
-9 + 9 + b = 6.403124237 + 9

Combine like terms: -9 + 9 = 0
0 + b = 6.403124237 + 9
b = 6.403124237 + 9

Combine like terms: 6.403124237 + 9 = 15.403124237
b = 15.403124237

Simplifying
b = 15.403124237


Subproblem 2
b + -9 = -6.403124237

Simplifying
b + -9 = -6.403124237

Reorder the terms:
-9 + b = -6.403124237

Solving
-9 + b = -6.403124237

Solving for variable 'b'.

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

Add '9' to each side of the equation.
-9 + 9 + b = -6.403124237 + 9

Combine like terms: -9 + 9 = 0
0 + b = -6.403124237 + 9
b = -6.403124237 + 9

Combine like terms: -6.403124237 + 9 = 2.596875763
b = 2.596875763

Simplifying
b = 2.596875763


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {15.403124237, 2.596875763}
Solution
b = {15.403124237, 2.596875763}

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