l^2-17l-289=0

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Solution for l^2-17l-289=0 equation:


Simplifying
l2 + -17l + -289 = 0

Reorder the terms:
-289 + -17l + l2 = 0

Solving
-289 + -17l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '289' to each side of the equation.
-289 + -17l + 289 + l2 = 0 + 289

Reorder the terms:
-289 + 289 + -17l + l2 = 0 + 289

Combine like terms: -289 + 289 = 0
0 + -17l + l2 = 0 + 289
-17l + l2 = 0 + 289

Combine like terms: 0 + 289 = 289
-17l + l2 = 289

The l term is -17l.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17l + 72.25 + l2 = 289 + 72.25

Reorder the terms:
72.25 + -17l + l2 = 289 + 72.25

Combine like terms: 289 + 72.25 = 361.25
72.25 + -17l + l2 = 361.25

Factor a perfect square on the left side:
(l + -8.5)(l + -8.5) = 361.25

Calculate the square root of the right side: 19.006577809

Break this problem into two subproblems by setting 
(l + -8.5) equal to 19.006577809 and -19.006577809.


Subproblem 1
l + -8.5 = 19.006577809

Simplifying
l + -8.5 = 19.006577809

Reorder the terms:
-8.5 + l = 19.006577809

Solving
-8.5 + l = 19.006577809

Solving for variable 'l'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + l = 19.006577809 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + l = 19.006577809 + 8.5
l = 19.006577809 + 8.5

Combine like terms: 19.006577809 + 8.5 = 27.506577809
l = 27.506577809

Simplifying
l = 27.506577809


Subproblem 2
l + -8.5 = -19.006577809

Simplifying
l + -8.5 = -19.006577809

Reorder the terms:
-8.5 + l = -19.006577809

Solving
-8.5 + l = -19.006577809

Solving for variable 'l'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + l = -19.006577809 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + l = -19.006577809 + 8.5
l = -19.006577809 + 8.5

Combine like terms: -19.006577809 + 8.5 = -10.506577809
l = -10.506577809

Simplifying
l = -10.506577809


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {27.506577809, -10.506577809}

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