l^2-30l-56=0

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Solution for l^2-30l-56=0 equation: 


Simplifying
l2 + -30l + -56 = 0

Reorder the terms:
-56 + -30l + l2 = 0

Solving
-56 + -30l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -30l + 56 + l2 = 0 + 56

Reorder the terms:
-56 + 56 + -30l + l2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -30l + l2 = 0 + 56
-30l + l2 = 0 + 56

Combine like terms: 0 + 56 = 56
-30l + l2 = 56

The l term is -30l.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30l + 225 + l2 = 56 + 225

Reorder the terms:
225 + -30l + l2 = 56 + 225

Combine like terms: 56 + 225 = 281
225 + -30l + l2 = 281

Factor a perfect square on the left side:
(l + -15)(l + -15) = 281

Calculate the square root of the right side: 16.763054614

Break this problem into two subproblems by setting 
(l + -15) equal to 16.763054614 and -16.763054614.


Subproblem 1
l + -15 = 16.763054614

Simplifying
l + -15 = 16.763054614

Reorder the terms:
-15 + l = 16.763054614

Solving
-15 + l = 16.763054614

Solving for variable 'l'.

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

Add '15' to each side of the equation.
-15 + 15 + l = 16.763054614 + 15

Combine like terms: -15 + 15 = 0
0 + l = 16.763054614 + 15
l = 16.763054614 + 15

Combine like terms: 16.763054614 + 15 = 31.763054614
l = 31.763054614

Simplifying
l = 31.763054614


Subproblem 2
l + -15 = -16.763054614

Simplifying
l + -15 = -16.763054614

Reorder the terms:
-15 + l = -16.763054614

Solving
-15 + l = -16.763054614

Solving for variable 'l'.

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

Add '15' to each side of the equation.
-15 + 15 + l = -16.763054614 + 15

Combine like terms: -15 + 15 = 0
0 + l = -16.763054614 + 15
l = -16.763054614 + 15

Combine like terms: -16.763054614 + 15 = -1.763054614
l = -1.763054614

Simplifying
l = -1.763054614


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {31.763054614, -1.763054614}

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