5b^2+32b+20=0

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Solution for 5b^2+32b+20=0 equation:


Simplifying
5b2 + 32b + 20 = 0

Reorder the terms:
20 + 32b + 5b2 = 0

Solving
20 + 32b + 5b2 = 0

Solving for variable 'b'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
4 + 6.4b + b2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6.4b + -4 + b2 = 0 + -4

Reorder the terms:
4 + -4 + 6.4b + b2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6.4b + b2 = 0 + -4
6.4b + b2 = 0 + -4

Combine like terms: 0 + -4 = -4
6.4b + b2 = -4

The b term is 6.4b.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4b + 10.24 + b2 = -4 + 10.24

Reorder the terms:
10.24 + 6.4b + b2 = -4 + 10.24

Combine like terms: -4 + 10.24 = 6.24
10.24 + 6.4b + b2 = 6.24

Factor a perfect square on the left side:
(b + 3.2)(b + 3.2) = 6.24

Calculate the square root of the right side: 2.497999199

Break this problem into two subproblems by setting 
(b + 3.2) equal to 2.497999199 and -2.497999199.

Subproblem 1

b + 3.2 = 2.497999199 Simplifying b + 3.2 = 2.497999199 Reorder the terms: 3.2 + b = 2.497999199 Solving 3.2 + b = 2.497999199 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + b = 2.497999199 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + b = 2.497999199 + -3.2 b = 2.497999199 + -3.2 Combine like terms: 2.497999199 + -3.2 = -0.702000801 b = -0.702000801 Simplifying b = -0.702000801

Subproblem 2

b + 3.2 = -2.497999199 Simplifying b + 3.2 = -2.497999199 Reorder the terms: 3.2 + b = -2.497999199 Solving 3.2 + b = -2.497999199 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + b = -2.497999199 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + b = -2.497999199 + -3.2 b = -2.497999199 + -3.2 Combine like terms: -2.497999199 + -3.2 = -5.697999199 b = -5.697999199 Simplifying b = -5.697999199

Solution

The solution to the problem is based on the solutions from the subproblems. b = {-0.702000801, -5.697999199}

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