l^2-5l=18

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Solution for l^2-5l=18 equation:


Simplifying
l2 + -5l = 18

Reorder the terms:
-5l + l2 = 18

Solving
-5l + l2 = 18

Solving for variable 'l'.

Reorder the terms:
-18 + -5l + l2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -5l + l2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -5l + 18 + l2 = 0 + 18

Reorder the terms:
-18 + 18 + -5l + l2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -5l + l2 = 0 + 18
-5l + l2 = 0 + 18

Combine like terms: 0 + 18 = 18
-5l + l2 = 18

The l term is -5l.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5l + 6.25 + l2 = 18 + 6.25

Reorder the terms:
6.25 + -5l + l2 = 18 + 6.25

Combine like terms: 18 + 6.25 = 24.25
6.25 + -5l + l2 = 24.25

Factor a perfect square on the left side:
(l + -2.5)(l + -2.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(l + -2.5) equal to 4.924428901 and -4.924428901.

Subproblem 1

l + -2.5 = 4.924428901 Simplifying l + -2.5 = 4.924428901 Reorder the terms: -2.5 + l = 4.924428901 Solving -2.5 + l = 4.924428901 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + l = 4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + l = 4.924428901 + 2.5 l = 4.924428901 + 2.5 Combine like terms: 4.924428901 + 2.5 = 7.424428901 l = 7.424428901 Simplifying l = 7.424428901

Subproblem 2

l + -2.5 = -4.924428901 Simplifying l + -2.5 = -4.924428901 Reorder the terms: -2.5 + l = -4.924428901 Solving -2.5 + l = -4.924428901 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + l = -4.924428901 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + l = -4.924428901 + 2.5 l = -4.924428901 + 2.5 Combine like terms: -4.924428901 + 2.5 = -2.424428901 l = -2.424428901 Simplifying l = -2.424428901

Solution

The solution to the problem is based on the solutions from the subproblems. l = {7.424428901, -2.424428901}

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