b^2+10b+5=0

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Solution for b^2+10b+5=0 equation: 


Simplifying
b2 + 10b + 5 = 0

Reorder the terms:
5 + 10b + b2 = 0

Solving
5 + 10b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 10b + -5 + b2 = 0 + -5

Reorder the terms:
5 + -5 + 10b + b2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 10b + b2 = 0 + -5
10b + b2 = 0 + -5

Combine like terms: 0 + -5 = -5
10b + b2 = -5

The b term is 10b.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10b + 25 + b2 = -5 + 25

Reorder the terms:
25 + 10b + b2 = -5 + 25

Combine like terms: -5 + 25 = 20
25 + 10b + b2 = 20

Factor a perfect square on the left side:
(b + 5)(b + 5) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(b + 5) equal to 4.472135955 and -4.472135955.


Subproblem 1
b + 5 = 4.472135955

Simplifying
b + 5 = 4.472135955

Reorder the terms:
5 + b = 4.472135955

Solving
5 + b = 4.472135955

Solving for variable 'b'.

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

Add '-5' to each side of the equation.
5 + -5 + b = 4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + b = 4.472135955 + -5
b = 4.472135955 + -5

Combine like terms: 4.472135955 + -5 = -0.527864045
b = -0.527864045

Simplifying
b = -0.527864045


Subproblem 2
b + 5 = -4.472135955

Simplifying
b + 5 = -4.472135955

Reorder the terms:
5 + b = -4.472135955

Solving
5 + b = -4.472135955

Solving for variable 'b'.

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

Add '-5' to each side of the equation.
5 + -5 + b = -4.472135955 + -5

Combine like terms: 5 + -5 = 0
0 + b = -4.472135955 + -5
b = -4.472135955 + -5

Combine like terms: -4.472135955 + -5 = -9.472135955
b = -9.472135955

Simplifying
b = -9.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {-0.527864045, -9.472135955}

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