L^2-29L=54

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Solution for L^2-29L=54 equation: 


Simplifying
L2 + -29L = 54

Reorder the terms:
-29L + L2 = 54

Solving
-29L + L2 = 54

Solving for variable 'L'.

Reorder the terms:
-54 + -29L + L2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -29L + L2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -29L + 54 + L2 = 0 + 54

Reorder the terms:
-54 + 54 + -29L + L2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -29L + L2 = 0 + 54
-29L + L2 = 0 + 54

Combine like terms: 0 + 54 = 54
-29L + L2 = 54

The L term is -29L.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29L + 210.25 + L2 = 54 + 210.25

Reorder the terms:
210.25 + -29L + L2 = 54 + 210.25

Combine like terms: 54 + 210.25 = 264.25
210.25 + -29L + L2 = 264.25

Factor a perfect square on the left side:
(L + -14.5)(L + -14.5) = 264.25

Calculate the square root of the right side: 16.255768207

Break this problem into two subproblems by setting 
(L + -14.5) equal to 16.255768207 and -16.255768207.


Subproblem 1
L + -14.5 = 16.255768207

Simplifying
L + -14.5 = 16.255768207

Reorder the terms:
-14.5 + L = 16.255768207

Solving
-14.5 + L = 16.255768207

Solving for variable 'L'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + L = 16.255768207 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + L = 16.255768207 + 14.5
L = 16.255768207 + 14.5

Combine like terms: 16.255768207 + 14.5 = 30.755768207
L = 30.755768207

Simplifying
L = 30.755768207


Subproblem 2
L + -14.5 = -16.255768207

Simplifying
L + -14.5 = -16.255768207

Reorder the terms:
-14.5 + L = -16.255768207

Solving
-14.5 + L = -16.255768207

Solving for variable 'L'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + L = -16.255768207 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + L = -16.255768207 + 14.5
L = -16.255768207 + 14.5

Combine like terms: -16.255768207 + 14.5 = -1.755768207
L = -1.755768207

Simplifying
L = -1.755768207


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {30.755768207, -1.755768207}

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