b^2+14b-48=0

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Solution for b^2+14b-48=0 equation: 


Simplifying
b2 + 14b + -48 = 0

Reorder the terms:
-48 + 14b + b2 = 0

Solving
-48 + 14b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 14b + 48 + b2 = 0 + 48

Reorder the terms:
-48 + 48 + 14b + b2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 14b + b2 = 0 + 48
14b + b2 = 0 + 48

Combine like terms: 0 + 48 = 48
14b + b2 = 48

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 = 48 + 49

Reorder the terms:
49 + 14b + b2 = 48 + 49

Combine like terms: 48 + 49 = 97
49 + 14b + b2 = 97

Factor a perfect square on the left side:
(b + 7)(b + 7) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(b + 7) equal to 9.848857802 and -9.848857802.


Subproblem 1
b + 7 = 9.848857802

Simplifying
b + 7 = 9.848857802

Reorder the terms:
7 + b = 9.848857802

Solving
7 + b = 9.848857802

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 = 9.848857802 + -7

Combine like terms: 7 + -7 = 0
0 + b = 9.848857802 + -7
b = 9.848857802 + -7

Combine like terms: 9.848857802 + -7 = 2.848857802
b = 2.848857802

Simplifying
b = 2.848857802


Subproblem 2
b + 7 = -9.848857802

Simplifying
b + 7 = -9.848857802

Reorder the terms:
7 + b = -9.848857802

Solving
7 + b = -9.848857802

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 = -9.848857802 + -7

Combine like terms: 7 + -7 = 0
0 + b = -9.848857802 + -7
b = -9.848857802 + -7

Combine like terms: -9.848857802 + -7 = -16.848857802
b = -16.848857802

Simplifying
b = -16.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {2.848857802, -16.848857802}

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