8b^2+28b-40=0

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Solution for 8b^2+28b-40=0 equation: 


Simplifying
8b2 + 28b + -40 = 0

Reorder the terms:
-40 + 28b + 8b2 = 0

Solving
-40 + 28b + 8b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 7b + 2b2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + 7b + 2b2)' equal to zero and attempt to solve:

Simplifying
-10 + 7b + 2b2 = 0

Solving
-10 + 7b + 2b2 = 0

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

Divide each side by '2'.
-5 + 3.5b + b2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 3.5b + 5 + b2 = 0 + 5

Reorder the terms:
-5 + 5 + 3.5b + b2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3.5b + b2 = 0 + 5
3.5b + b2 = 0 + 5

Combine like terms: 0 + 5 = 5
3.5b + b2 = 5

The b term is 3.5b.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5b + 3.0625 + b2 = 5 + 3.0625

Reorder the terms:
3.0625 + 3.5b + b2 = 5 + 3.0625

Combine like terms: 5 + 3.0625 = 8.0625
3.0625 + 3.5b + b2 = 8.0625

Factor a perfect square on the left side:
(b + 1.75)(b + 1.75) = 8.0625

Calculate the square root of the right side: 2.839454173

Break this problem into two subproblems by setting 
(b + 1.75) equal to 2.839454173 and -2.839454173.


Subproblem 1
b + 1.75 = 2.839454173

Simplifying
b + 1.75 = 2.839454173

Reorder the terms:
1.75 + b = 2.839454173

Solving
1.75 + b = 2.839454173

Solving for variable 'b'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + b = 2.839454173 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + b = 2.839454173 + -1.75
b = 2.839454173 + -1.75

Combine like terms: 2.839454173 + -1.75 = 1.089454173
b = 1.089454173

Simplifying
b = 1.089454173


Subproblem 2
b + 1.75 = -2.839454173

Simplifying
b + 1.75 = -2.839454173

Reorder the terms:
1.75 + b = -2.839454173

Solving
1.75 + b = -2.839454173

Solving for variable 'b'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + b = -2.839454173 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + b = -2.839454173 + -1.75
b = -2.839454173 + -1.75

Combine like terms: -2.839454173 + -1.75 = -4.589454173
b = -4.589454173

Simplifying
b = -4.589454173


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.089454173, -4.589454173}
Solution
b = {1.089454173, -4.589454173}

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