b^2+5b-320=0

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Solution for b^2+5b-320=0 equation: 


Simplifying
b2 + 5b + -320 = 0

Reorder the terms:
-320 + 5b + b2 = 0

Solving
-320 + 5b + b2 = 0

Solving for variable 'b'.

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 5b + 320 + b2 = 0 + 320

Reorder the terms:
-320 + 320 + 5b + b2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 5b + b2 = 0 + 320
5b + b2 = 0 + 320

Combine like terms: 0 + 320 = 320
5b + b2 = 320

The b term is 5b.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5b + 6.25 + b2 = 320 + 6.25

Reorder the terms:
6.25 + 5b + b2 = 320 + 6.25

Combine like terms: 320 + 6.25 = 326.25
6.25 + 5b + b2 = 326.25

Factor a perfect square on the left side:
(b + 2.5)(b + 2.5) = 326.25

Calculate the square root of the right side: 18.062391868

Break this problem into two subproblems by setting 
(b + 2.5) equal to 18.062391868 and -18.062391868.


Subproblem 1
b + 2.5 = 18.062391868

Simplifying
b + 2.5 = 18.062391868

Reorder the terms:
2.5 + b = 18.062391868

Solving
2.5 + b = 18.062391868

Solving for variable 'b'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + b = 18.062391868 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + b = 18.062391868 + -2.5
b = 18.062391868 + -2.5

Combine like terms: 18.062391868 + -2.5 = 15.562391868
b = 15.562391868

Simplifying
b = 15.562391868


Subproblem 2
b + 2.5 = -18.062391868

Simplifying
b + 2.5 = -18.062391868

Reorder the terms:
2.5 + b = -18.062391868

Solving
2.5 + b = -18.062391868

Solving for variable 'b'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + b = -18.062391868 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + b = -18.062391868 + -2.5
b = -18.062391868 + -2.5

Combine like terms: -18.062391868 + -2.5 = -20.562391868
b = -20.562391868

Simplifying
b = -20.562391868


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {15.562391868, -20.562391868}

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