l^2-18l-80=0

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Solution for l^2-18l-80=0 equation: 


Simplifying
l2 + -18l + -80 = 0

Reorder the terms:
-80 + -18l + l2 = 0

Solving
-80 + -18l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -18l + 80 + l2 = 0 + 80

Reorder the terms:
-80 + 80 + -18l + l2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -18l + l2 = 0 + 80
-18l + l2 = 0 + 80

Combine like terms: 0 + 80 = 80
-18l + l2 = 80

The l term is -18l.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18l + 81 + l2 = 80 + 81

Reorder the terms:
81 + -18l + l2 = 80 + 81

Combine like terms: 80 + 81 = 161
81 + -18l + l2 = 161

Factor a perfect square on the left side:
(l + -9)(l + -9) = 161

Calculate the square root of the right side: 12.68857754

Break this problem into two subproblems by setting 
(l + -9) equal to 12.68857754 and -12.68857754.


Subproblem 1
l + -9 = 12.68857754

Simplifying
l + -9 = 12.68857754

Reorder the terms:
-9 + l = 12.68857754

Solving
-9 + l = 12.68857754

Solving for variable 'l'.

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

Add '9' to each side of the equation.
-9 + 9 + l = 12.68857754 + 9

Combine like terms: -9 + 9 = 0
0 + l = 12.68857754 + 9
l = 12.68857754 + 9

Combine like terms: 12.68857754 + 9 = 21.68857754
l = 21.68857754

Simplifying
l = 21.68857754


Subproblem 2
l + -9 = -12.68857754

Simplifying
l + -9 = -12.68857754

Reorder the terms:
-9 + l = -12.68857754

Solving
-9 + l = -12.68857754

Solving for variable 'l'.

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

Add '9' to each side of the equation.
-9 + 9 + l = -12.68857754 + 9

Combine like terms: -9 + 9 = 0
0 + l = -12.68857754 + 9
l = -12.68857754 + 9

Combine like terms: -12.68857754 + 9 = -3.68857754
l = -3.68857754

Simplifying
l = -3.68857754


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {21.68857754, -3.68857754}

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