L(L-3.5)=11.76

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Solution for L(L-3.5)=11.76 equation: 


Simplifying
L(L + -3.5) = 11.76

Reorder the terms:
L(-3.5 + L) = 11.76
(-3.5 * L + L * L) = 11.76
(-3.5L + L2) = 11.76

Solving
-3.5L + L2 = 11.76

Solving for variable 'L'.

Reorder the terms:
-11.76 + -3.5L + L2 = 11.76 + -11.76

Combine like terms: 11.76 + -11.76 = 0.00
-11.76 + -3.5L + L2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '11.76' to each side of the equation.
-11.76 + -3.5L + 11.76 + L2 = 0.00 + 11.76

Reorder the terms:
-11.76 + 11.76 + -3.5L + L2 = 0.00 + 11.76

Combine like terms: -11.76 + 11.76 = 0.00
0.00 + -3.5L + L2 = 0.00 + 11.76
-3.5L + L2 = 0.00 + 11.76

Combine like terms: 0.00 + 11.76 = 11.76
-3.5L + L2 = 11.76

The L term is -3.5L.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5L + 3.0625 + L2 = 11.76 + 3.0625

Reorder the terms:
3.0625 + -3.5L + L2 = 11.76 + 3.0625

Combine like terms: 11.76 + 3.0625 = 14.8225
3.0625 + -3.5L + L2 = 14.8225

Factor a perfect square on the left side:
(L + -1.75)(L + -1.75) = 14.8225

Calculate the square root of the right side: 3.85

Break this problem into two subproblems by setting 
(L + -1.75) equal to 3.85 and -3.85.


Subproblem 1
L + -1.75 = 3.85

Simplifying
L + -1.75 = 3.85

Reorder the terms:
-1.75 + L = 3.85

Solving
-1.75 + L = 3.85

Solving for variable 'L'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + L = 3.85 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + L = 3.85 + 1.75
L = 3.85 + 1.75

Combine like terms: 3.85 + 1.75 = 5.6
L = 5.6

Simplifying
L = 5.6


Subproblem 2
L + -1.75 = -3.85

Simplifying
L + -1.75 = -3.85

Reorder the terms:
-1.75 + L = -3.85

Solving
-1.75 + L = -3.85

Solving for variable 'L'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + L = -3.85 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + L = -3.85 + 1.75
L = -3.85 + 1.75

Combine like terms: -3.85 + 1.75 = -2.1
L = -2.1

Simplifying
L = -2.1


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {5.6, -2.1}

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