b^2+15-14b=0

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Solution for b^2+15-14b=0 equation:


Simplifying
b2 + 15 + -14b = 0

Reorder the terms:
15 + -14b + b2 = 0

Solving
15 + -14b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -14b + -15 + b2 = 0 + -15

Reorder the terms:
15 + -15 + -14b + b2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -14b + b2 = 0 + -15
-14b + b2 = 0 + -15

Combine like terms: 0 + -15 = -15
-14b + b2 = -15

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 = -15 + 49

Reorder the terms:
49 + -14b + b2 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + -14b + b2 = 34

Factor a perfect square on the left side:
(b + -7)(b + -7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(b + -7) equal to 5.830951895 and -5.830951895.


Subproblem 1
b + -7 = 5.830951895

Simplifying
b + -7 = 5.830951895

Reorder the terms:
-7 + b = 5.830951895

Solving
-7 + b = 5.830951895

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 = 5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + b = 5.830951895 + 7
b = 5.830951895 + 7

Combine like terms: 5.830951895 + 7 = 12.830951895
b = 12.830951895

Simplifying
b = 12.830951895


Subproblem 2
b + -7 = -5.830951895

Simplifying
b + -7 = -5.830951895

Reorder the terms:
-7 + b = -5.830951895

Solving
-7 + b = -5.830951895

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 = -5.830951895 + 7

Combine like terms: -7 + 7 = 0
0 + b = -5.830951895 + 7
b = -5.830951895 + 7

Combine like terms: -5.830951895 + 7 = 1.169048105
b = 1.169048105

Simplifying
b = 1.169048105


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {12.830951895, 1.169048105}

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