(b^2+14b+49)=5

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Solution for (b^2+14b+49)=5 equation:


Simplifying
(b2 + 14b + 49) = 5

Reorder the terms:
(49 + 14b + b2) = 5

Remove parenthesis around (49 + 14b + b2)
49 + 14b + b2 = 5

Solving
49 + 14b + b2 = 5

Solving for variable 'b'.

Reorder the terms:
49 + -5 + 14b + b2 = 5 + -5

Combine like terms: 49 + -5 = 44
44 + 14b + b2 = 5 + -5

Combine like terms: 5 + -5 = 0
44 + 14b + b2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + 14b + -44 + b2 = 0 + -44

Reorder the terms:
44 + -44 + 14b + b2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 14b + b2 = 0 + -44
14b + b2 = 0 + -44

Combine like terms: 0 + -44 = -44
14b + b2 = -44

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 = -44 + 49

Reorder the terms:
49 + 14b + b2 = -44 + 49

Combine like terms: -44 + 49 = 5
49 + 14b + b2 = 5

Factor a perfect square on the left side:
(b + 7)(b + 7) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(b + 7) equal to 2.236067978 and -2.236067978.

Subproblem 1

b + 7 = 2.236067978 Simplifying b + 7 = 2.236067978 Reorder the terms: 7 + b = 2.236067978 Solving 7 + b = 2.236067978 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 = 2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + b = 2.236067978 + -7 b = 2.236067978 + -7 Combine like terms: 2.236067978 + -7 = -4.763932022 b = -4.763932022 Simplifying b = -4.763932022

Subproblem 2

b + 7 = -2.236067978 Simplifying b + 7 = -2.236067978 Reorder the terms: 7 + b = -2.236067978 Solving 7 + b = -2.236067978 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 = -2.236067978 + -7 Combine like terms: 7 + -7 = 0 0 + b = -2.236067978 + -7 b = -2.236067978 + -7 Combine like terms: -2.236067978 + -7 = -9.236067978 b = -9.236067978 Simplifying b = -9.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-4.763932022, -9.236067978}

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