b^2-14b-56=0

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Solution for b^2-14b-56=0 equation: 


Simplifying
b2 + -14b + -56 = 0

Reorder the terms:
-56 + -14b + b2 = 0

Solving
-56 + -14b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -14b + 56 + b2 = 0 + 56

Reorder the terms:
-56 + 56 + -14b + b2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -14b + b2 = 0 + 56
-14b + b2 = 0 + 56

Combine like terms: 0 + 56 = 56
-14b + b2 = 56

The b term is -14b.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14b + 49 + b2 = 56 + 49

Reorder the terms:
49 + -14b + b2 = 56 + 49

Combine like terms: 56 + 49 = 105
49 + -14b + b2 = 105

Factor a perfect square on the left side:
(b + -7)(b + -7) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(b + -7) equal to 10.246950766 and -10.246950766.


Subproblem 1
b + -7 = 10.246950766

Simplifying
b + -7 = 10.246950766

Reorder the terms:
-7 + b = 10.246950766

Solving
-7 + b = 10.246950766

Solving for variable 'b'.

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

Add '7' to each side of the equation.
-7 + 7 + b = 10.246950766 + 7

Combine like terms: -7 + 7 = 0
0 + b = 10.246950766 + 7
b = 10.246950766 + 7

Combine like terms: 10.246950766 + 7 = 17.246950766
b = 17.246950766

Simplifying
b = 17.246950766


Subproblem 2
b + -7 = -10.246950766

Simplifying
b + -7 = -10.246950766

Reorder the terms:
-7 + b = -10.246950766

Solving
-7 + b = -10.246950766

Solving for variable 'b'.

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

Add '7' to each side of the equation.
-7 + 7 + b = -10.246950766 + 7

Combine like terms: -7 + 7 = 0
0 + b = -10.246950766 + 7
b = -10.246950766 + 7

Combine like terms: -10.246950766 + 7 = -3.246950766
b = -3.246950766

Simplifying
b = -3.246950766


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {17.246950766, -3.246950766}

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