b^2+7b-16=0

Solution for b^2+7b-16=0 equation:

Simplifying
b2 + 7b + -16 = 0

Reorder the terms:
-16 + 7b + b2 = 0

Solving
-16 + 7b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 7b + 16 + b2 = 0 + 16

Reorder the terms:
-16 + 16 + 7b + b2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 7b + b2 = 0 + 16
7b + b2 = 0 + 16

Combine like terms: 0 + 16 = 16
7b + b2 = 16

The b term is 7b.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7b + 12.25 + b2 = 16 + 12.25

Reorder the terms:
12.25 + 7b + b2 = 16 + 12.25

Combine like terms: 16 + 12.25 = 28.25
12.25 + 7b + b2 = 28.25

Factor a perfect square on the left side:
(b + 3.5)(b + 3.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(b + 3.5) equal to 5.315072906 and -5.315072906.

Subproblem 1
b + 3.5 = 5.315072906

Simplifying
b + 3.5 = 5.315072906

Reorder the terms:
3.5 + b = 5.315072906

Solving
3.5 + b = 5.315072906

Solving for variable 'b'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + b = 5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + b = 5.315072906 + -3.5
b = 5.315072906 + -3.5

Combine like terms: 5.315072906 + -3.5 = 1.815072906
b = 1.815072906

Simplifying
b = 1.815072906

Subproblem 2
b + 3.5 = -5.315072906

Simplifying
b + 3.5 = -5.315072906

Reorder the terms:
3.5 + b = -5.315072906

Solving
3.5 + b = -5.315072906

Solving for variable 'b'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + b = -5.315072906 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + b = -5.315072906 + -3.5
b = -5.315072906 + -3.5

Combine like terms: -5.315072906 + -3.5 = -8.815072906
b = -8.815072906

Simplifying
b = -8.815072906

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.815072906, -8.815072906}