2l^2-5l=324

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Solution for 2l^2-5l=324 equation:


Simplifying
2l2 + -5l = 324

Reorder the terms:
-5l + 2l2 = 324

Solving
-5l + 2l2 = 324

Solving for variable 'l'.

Reorder the terms:
-324 + -5l + 2l2 = 324 + -324

Combine like terms: 324 + -324 = 0
-324 + -5l + 2l2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-162 + -2.5l + l2 = 0

Move the constant term to the right:

Add '162' to each side of the equation.
-162 + -2.5l + 162 + l2 = 0 + 162

Reorder the terms:
-162 + 162 + -2.5l + l2 = 0 + 162

Combine like terms: -162 + 162 = 0
0 + -2.5l + l2 = 0 + 162
-2.5l + l2 = 0 + 162

Combine like terms: 0 + 162 = 162
-2.5l + l2 = 162

The l term is -2.5l.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5l + 1.5625 + l2 = 162 + 1.5625

Reorder the terms:
1.5625 + -2.5l + l2 = 162 + 1.5625

Combine like terms: 162 + 1.5625 = 163.5625
1.5625 + -2.5l + l2 = 163.5625

Factor a perfect square on the left side:
(l + -1.25)(l + -1.25) = 163.5625

Calculate the square root of the right side: 12.789155562

Break this problem into two subproblems by setting 
(l + -1.25) equal to 12.789155562 and -12.789155562.

Subproblem 1

l + -1.25 = 12.789155562 Simplifying l + -1.25 = 12.789155562 Reorder the terms: -1.25 + l = 12.789155562 Solving -1.25 + l = 12.789155562 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + l = 12.789155562 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + l = 12.789155562 + 1.25 l = 12.789155562 + 1.25 Combine like terms: 12.789155562 + 1.25 = 14.039155562 l = 14.039155562 Simplifying l = 14.039155562

Subproblem 2

l + -1.25 = -12.789155562 Simplifying l + -1.25 = -12.789155562 Reorder the terms: -1.25 + l = -12.789155562 Solving -1.25 + l = -12.789155562 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + l = -12.789155562 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + l = -12.789155562 + 1.25 l = -12.789155562 + 1.25 Combine like terms: -12.789155562 + 1.25 = -11.539155562 l = -11.539155562 Simplifying l = -11.539155562

Solution

The solution to the problem is based on the solutions from the subproblems. l = {14.039155562, -11.539155562}

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