2l^2-158l=600

Solution for 2l^2-158l=600 equation:

Simplifying
2l2 + -158l = 600

Reorder the terms:
-158l + 2l2 = 600

Solving
-158l + 2l2 = 600

Solving for variable 'l'.

Reorder the terms:
-600 + -158l + 2l2 = 600 + -600

Combine like terms: 600 + -600 = 0
-600 + -158l + 2l2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + -79l + l2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-300 + -79l + l2)' equal to zero and attempt to solve:

Simplifying
-300 + -79l + l2 = 0

Solving
-300 + -79l + l2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + -79l + 300 + l2 = 0 + 300

Reorder the terms:
-300 + 300 + -79l + l2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + -79l + l2 = 0 + 300
-79l + l2 = 0 + 300

Combine like terms: 0 + 300 = 300
-79l + l2 = 300

The l term is -79l.  Take half its coefficient (-39.5).
Square it (1560.25) and add it to both sides.

Add '1560.25' to each side of the equation.
-79l + 1560.25 + l2 = 300 + 1560.25

Reorder the terms:
1560.25 + -79l + l2 = 300 + 1560.25

Combine like terms: 300 + 1560.25 = 1860.25
1560.25 + -79l + l2 = 1860.25

Factor a perfect square on the left side:
(l + -39.5)(l + -39.5) = 1860.25

Calculate the square root of the right side: 43.130615576

Break this problem into two subproblems by setting 
(l + -39.5) equal to 43.130615576 and -43.130615576.

Subproblem 1
l + -39.5 = 43.130615576

Simplifying
l + -39.5 = 43.130615576

Reorder the terms:
-39.5 + l = 43.130615576

Solving
-39.5 + l = 43.130615576

Solving for variable 'l'.

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

Add '39.5' to each side of the equation.
-39.5 + 39.5 + l = 43.130615576 + 39.5

Combine like terms: -39.5 + 39.5 = 0.0
0.0 + l = 43.130615576 + 39.5
l = 43.130615576 + 39.5

Combine like terms: 43.130615576 + 39.5 = 82.630615576
l = 82.630615576

Simplifying
l = 82.630615576

Subproblem 2
l + -39.5 = -43.130615576

Simplifying
l + -39.5 = -43.130615576

Reorder the terms:
-39.5 + l = -43.130615576

Solving
-39.5 + l = -43.130615576

Solving for variable 'l'.

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

Add '39.5' to each side of the equation.
-39.5 + 39.5 + l = -43.130615576 + 39.5

Combine like terms: -39.5 + 39.5 = 0.0
0.0 + l = -43.130615576 + 39.5
l = -43.130615576 + 39.5

Combine like terms: -43.130615576 + 39.5 = -3.630615576
l = -3.630615576

Simplifying
l = -3.630615576

Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {82.630615576, -3.630615576}
Solution
l = {82.630615576, -3.630615576}