L^2-8L-7200=0

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Solution for L^2-8L-7200=0 equation: 


Simplifying
L2 + -8L + -7200 = 0

Reorder the terms:
-7200 + -8L + L2 = 0

Solving
-7200 + -8L + L2 = 0

Solving for variable 'L'.

Begin completing the square.

Move the constant term to the right:

Add '7200' to each side of the equation.
-7200 + -8L + 7200 + L2 = 0 + 7200

Reorder the terms:
-7200 + 7200 + -8L + L2 = 0 + 7200

Combine like terms: -7200 + 7200 = 0
0 + -8L + L2 = 0 + 7200
-8L + L2 = 0 + 7200

Combine like terms: 0 + 7200 = 7200
-8L + L2 = 7200

The L term is -8L.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8L + 16 + L2 = 7200 + 16

Reorder the terms:
16 + -8L + L2 = 7200 + 16

Combine like terms: 7200 + 16 = 7216
16 + -8L + L2 = 7216

Factor a perfect square on the left side:
(L + -4)(L + -4) = 7216

Calculate the square root of the right side: 84.947042326

Break this problem into two subproblems by setting 
(L + -4) equal to 84.947042326 and -84.947042326.


Subproblem 1
L + -4 = 84.947042326

Simplifying
L + -4 = 84.947042326

Reorder the terms:
-4 + L = 84.947042326

Solving
-4 + L = 84.947042326

Solving for variable 'L'.

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

Add '4' to each side of the equation.
-4 + 4 + L = 84.947042326 + 4

Combine like terms: -4 + 4 = 0
0 + L = 84.947042326 + 4
L = 84.947042326 + 4

Combine like terms: 84.947042326 + 4 = 88.947042326
L = 88.947042326

Simplifying
L = 88.947042326


Subproblem 2
L + -4 = -84.947042326

Simplifying
L + -4 = -84.947042326

Reorder the terms:
-4 + L = -84.947042326

Solving
-4 + L = -84.947042326

Solving for variable 'L'.

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

Add '4' to each side of the equation.
-4 + 4 + L = -84.947042326 + 4

Combine like terms: -4 + 4 = 0
0 + L = -84.947042326 + 4
L = -84.947042326 + 4

Combine like terms: -84.947042326 + 4 = -80.947042326
L = -80.947042326

Simplifying
L = -80.947042326


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {88.947042326, -80.947042326}

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