112896*L=3186376.7-7902.72*L+4.90L^2

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Solution for 112896*L=3186376.7-7902.72*L+4.90L^2 equation:


Simplifying
112896L = 3186376.7 + -7902.72L + 4.90L2

Solving
112896L = 3186376.7 + -7902.72L + 4.90L2

Solving for variable 'L'.

Reorder the terms:
-3186376.7 + 112896L + 7902.72L + -4.90L2 = 3186376.7 + -7902.72L + 4.90L2 + -3186376.7 + 7902.72L + -4.90L2

Combine like terms: 112896L + 7902.72L = 120798.72L
-3186376.7 + 120798.72L + -4.90L2 = 3186376.7 + -7902.72L + 4.90L2 + -3186376.7 + 7902.72L + -4.90L2

Reorder the terms:
-3186376.7 + 120798.72L + -4.90L2 = 3186376.7 + -3186376.7 + -7902.72L + 7902.72L + 4.90L2 + -4.90L2

Combine like terms: 3186376.7 + -3186376.7 = 0.0
-3186376.7 + 120798.72L + -4.90L2 = 0.0 + -7902.72L + 7902.72L + 4.90L2 + -4.90L2
-3186376.7 + 120798.72L + -4.90L2 = -7902.72L + 7902.72L + 4.90L2 + -4.90L2

Combine like terms: -7902.72L + 7902.72L = 0.00
-3186376.7 + 120798.72L + -4.90L2 = 0.00 + 4.90L2 + -4.90L2
-3186376.7 + 120798.72L + -4.90L2 = 4.90L2 + -4.90L2

Combine like terms: 4.90L2 + -4.90L2 = 0.00
-3186376.7 + 120798.72L + -4.90L2 = 0.00

Begin completing the square.  Divide all terms by
-4.90 the coefficient of the squared term: 

Divide each side by '-4.90'.
650280.9592 + -24652.8L + L2 = 0

Move the constant term to the right:

Add '-650280.9592' to each side of the equation.
650280.9592 + -24652.8L + -650280.9592 + L2 = 0 + -650280.9592

Reorder the terms:
650280.9592 + -650280.9592 + -24652.8L + L2 = 0 + -650280.9592

Combine like terms: 650280.9592 + -650280.9592 = 0.0000
0.0000 + -24652.8L + L2 = 0 + -650280.9592
-24652.8L + L2 = 0 + -650280.9592

Combine like terms: 0 + -650280.9592 = -650280.9592
-24652.8L + L2 = -650280.9592

The L term is -24652.8L.  Take half its coefficient (-12326.4).
Square it (151940137.0) and add it to both sides.

Add '151940137.0' to each side of the equation.
-24652.8L + 151940137.0 + L2 = -650280.9592 + 151940137.0

Reorder the terms:
151940137.0 + -24652.8L + L2 = -650280.9592 + 151940137.0

Combine like terms: -650280.9592 + 151940137.0 = 151289856.0408
151940137.0 + -24652.8L + L2 = 151289856.0408

Factor a perfect square on the left side:
(L + -12326.4)(L + -12326.4) = 151289856.0408

Calculate the square root of the right side: 12299.994147999

Break this problem into two subproblems by setting 
(L + -12326.4) equal to 12299.994147999 and -12299.994147999.


Subproblem 1
L + -12326.4 = 12299.994147999

Simplifying
L + -12326.4 = 12299.994147999

Reorder the terms:
-12326.4 + L = 12299.994147999

Solving
-12326.4 + L = 12299.994147999

Solving for variable 'L'.

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

Add '12326.4' to each side of the equation.
-12326.4 + 12326.4 + L = 12299.994147999 + 12326.4

Combine like terms: -12326.4 + 12326.4 = 0.0
0.0 + L = 12299.994147999 + 12326.4
L = 12299.994147999 + 12326.4

Combine like terms: 12299.994147999 + 12326.4 = 24626.394147999
L = 24626.394147999

Simplifying
L = 24626.394147999


Subproblem 2
L + -12326.4 = -12299.994147999

Simplifying
L + -12326.4 = -12299.994147999

Reorder the terms:
-12326.4 + L = -12299.994147999

Solving
-12326.4 + L = -12299.994147999

Solving for variable 'L'.

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

Add '12326.4' to each side of the equation.
-12326.4 + 12326.4 + L = -12299.994147999 + 12326.4

Combine like terms: -12326.4 + 12326.4 = 0.0
0.0 + L = -12299.994147999 + 12326.4
L = -12299.994147999 + 12326.4

Combine like terms: -12299.994147999 + 12326.4 = 26.405852001
L = 26.405852001

Simplifying
L = 26.405852001


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {24626.394147999, 26.405852001}

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