b^2-7b-6=0

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Solution for b^2-7b-6=0 equation: 


Simplifying
b2 + -7b + -6 = 0

Reorder the terms:
-6 + -7b + b2 = 0

Solving
-6 + -7b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -7b + 6 + b2 = 0 + 6

Reorder the terms:
-6 + 6 + -7b + b2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -7b + b2 = 0 + 6
-7b + b2 = 0 + 6

Combine like terms: 0 + 6 = 6
-7b + b2 = 6

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 = 6 + 12.25

Reorder the terms:
12.25 + -7b + b2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + -7b + b2 = 18.25

Factor a perfect square on the left side:
(b + -3.5)(b + -3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(b + -3.5) equal to 4.272001873 and -4.272001873.


Subproblem 1
b + -3.5 = 4.272001873

Simplifying
b + -3.5 = 4.272001873

Reorder the terms:
-3.5 + b = 4.272001873

Solving
-3.5 + b = 4.272001873

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 = 4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + b = 4.272001873 + 3.5
b = 4.272001873 + 3.5

Combine like terms: 4.272001873 + 3.5 = 7.772001873
b = 7.772001873

Simplifying
b = 7.772001873


Subproblem 2
b + -3.5 = -4.272001873

Simplifying
b + -3.5 = -4.272001873

Reorder the terms:
-3.5 + b = -4.272001873

Solving
-3.5 + b = -4.272001873

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 = -4.272001873 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + b = -4.272001873 + 3.5
b = -4.272001873 + 3.5

Combine like terms: -4.272001873 + 3.5 = -0.772001873
b = -0.772001873

Simplifying
b = -0.772001873


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {7.772001873, -0.772001873}

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