l^2+4l=100

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Solution for l^2+4l=100 equation: 


Simplifying
l2 + 4l = 100

Reorder the terms:
4l + l2 = 100

Solving
4l + l2 = 100

Solving for variable 'l'.

Reorder the terms:
-100 + 4l + l2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 4l + l2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 4l + 100 + l2 = 0 + 100

Reorder the terms:
-100 + 100 + 4l + l2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 4l + l2 = 0 + 100
4l + l2 = 0 + 100

Combine like terms: 0 + 100 = 100
4l + l2 = 100

The l term is 4l.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4l + 4 + l2 = 100 + 4

Reorder the terms:
4 + 4l + l2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + 4l + l2 = 104

Factor a perfect square on the left side:
(l + 2)(l + 2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(l + 2) equal to 10.198039027 and -10.198039027.


Subproblem 1
l + 2 = 10.198039027

Simplifying
l + 2 = 10.198039027

Reorder the terms:
2 + l = 10.198039027

Solving
2 + l = 10.198039027

Solving for variable 'l'.

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

Add '-2' to each side of the equation.
2 + -2 + l = 10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + l = 10.198039027 + -2
l = 10.198039027 + -2

Combine like terms: 10.198039027 + -2 = 8.198039027
l = 8.198039027

Simplifying
l = 8.198039027


Subproblem 2
l + 2 = -10.198039027

Simplifying
l + 2 = -10.198039027

Reorder the terms:
2 + l = -10.198039027

Solving
2 + l = -10.198039027

Solving for variable 'l'.

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

Add '-2' to each side of the equation.
2 + -2 + l = -10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + l = -10.198039027 + -2
l = -10.198039027 + -2

Combine like terms: -10.198039027 + -2 = -12.198039027
l = -12.198039027

Simplifying
l = -12.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {8.198039027, -12.198039027}

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