L^2+0.04L-0.00052=0

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Solution for L^2+0.04L-0.00052=0 equation: 


Simplifying
L2 + 0.04L + -0.00052 = 0

Reorder the terms:
-0.00052 + 0.04L + L2 = 0

Solving
-0.00052 + 0.04L + L2 = 0

Solving for variable 'L'.

Begin completing the square.

Move the constant term to the right:

Add '0.00052' to each side of the equation.
-0.00052 + 0.04L + 0.00052 + L2 = 0 + 0.00052

Reorder the terms:
-0.00052 + 0.00052 + 0.04L + L2 = 0 + 0.00052

Combine like terms: -0.00052 + 0.00052 = 0.00000
0.00000 + 0.04L + L2 = 0 + 0.00052
0.04L + L2 = 0 + 0.00052

Combine like terms: 0 + 0.00052 = 0.00052
0.04L + L2 = 0.00052

The L term is 0.04L.  Take half its coefficient (0.02).
Square it (0.0004) and add it to both sides.

Add '0.0004' to each side of the equation.
0.04L + 0.0004 + L2 = 0.00052 + 0.0004

Reorder the terms:
0.0004 + 0.04L + L2 = 0.00052 + 0.0004

Combine like terms: 0.00052 + 0.0004 = 0.00092
0.0004 + 0.04L + L2 = 0.00092

Factor a perfect square on the left side:
(L + 0.02)(L + 0.02) = 0.00092

Calculate the square root of the right side: 0.030331502

Break this problem into two subproblems by setting 
(L + 0.02) equal to 0.030331502 and -0.030331502.


Subproblem 1
L + 0.02 = 0.030331502

Simplifying
L + 0.02 = 0.030331502

Reorder the terms:
0.02 + L = 0.030331502

Solving
0.02 + L = 0.030331502

Solving for variable 'L'.

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

Add '-0.02' to each side of the equation.
0.02 + -0.02 + L = 0.030331502 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + L = 0.030331502 + -0.02
L = 0.030331502 + -0.02

Combine like terms: 0.030331502 + -0.02 = 0.010331502
L = 0.010331502

Simplifying
L = 0.010331502


Subproblem 2
L + 0.02 = -0.030331502

Simplifying
L + 0.02 = -0.030331502

Reorder the terms:
0.02 + L = -0.030331502

Solving
0.02 + L = -0.030331502

Solving for variable 'L'.

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

Add '-0.02' to each side of the equation.
0.02 + -0.02 + L = -0.030331502 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + L = -0.030331502 + -0.02
L = -0.030331502 + -0.02

Combine like terms: -0.030331502 + -0.02 = -0.050331502
L = -0.050331502

Simplifying
L = -0.050331502


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {0.010331502, -0.050331502}

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