L^2+5L-320=0

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


Simplifying
L2 + 5L + -320 = 0

Reorder the terms:
-320 + 5L + L2 = 0

Solving
-320 + 5L + L2 = 0

Solving for variable 'L'.

Begin completing the square.

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 5L + 320 + L2 = 0 + 320

Reorder the terms:
-320 + 320 + 5L + L2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 5L + L2 = 0 + 320
5L + L2 = 0 + 320

Combine like terms: 0 + 320 = 320
5L + L2 = 320

The L term is 5L.  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.
5L + 6.25 + L2 = 320 + 6.25

Reorder the terms:
6.25 + 5L + L2 = 320 + 6.25

Combine like terms: 320 + 6.25 = 326.25
6.25 + 5L + L2 = 326.25

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

Calculate the square root of the right side: 18.062391868

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


Subproblem 1
L + 2.5 = 18.062391868

Simplifying
L + 2.5 = 18.062391868

Reorder the terms:
2.5 + L = 18.062391868

Solving
2.5 + L = 18.062391868

Solving for variable 'L'.

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

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

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

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

Simplifying
L = 15.562391868


Subproblem 2
L + 2.5 = -18.062391868

Simplifying
L + 2.5 = -18.062391868

Reorder the terms:
2.5 + L = -18.062391868

Solving
2.5 + L = -18.062391868

Solving for variable 'L'.

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

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

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

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

Simplifying
L = -20.562391868


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

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