l^2+2l=100

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Solution for l^2+2l=100 equation:


Simplifying
l2 + 2l = 100

Reorder the terms:
2l + l2 = 100

Solving
2l + l2 = 100

Solving for variable 'l'.

Reorder the terms:
-100 + 2l + l2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 2l + l2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 2l + 100 + l2 = 0 + 100

Reorder the terms:
-100 + 100 + 2l + l2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 2l + l2 = 0 + 100
2l + l2 = 0 + 100

Combine like terms: 0 + 100 = 100
2l + l2 = 100

The l term is 2l.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2l + 1 + l2 = 100 + 1

Reorder the terms:
1 + 2l + l2 = 100 + 1

Combine like terms: 100 + 1 = 101
1 + 2l + l2 = 101

Factor a perfect square on the left side:
(l + 1)(l + 1) = 101

Calculate the square root of the right side: 10.049875621

Break this problem into two subproblems by setting 
(l + 1) equal to 10.049875621 and -10.049875621.

Subproblem 1

l + 1 = 10.049875621 Simplifying l + 1 = 10.049875621 Reorder the terms: 1 + l = 10.049875621 Solving 1 + l = 10.049875621 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + l = 10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + l = 10.049875621 + -1 l = 10.049875621 + -1 Combine like terms: 10.049875621 + -1 = 9.049875621 l = 9.049875621 Simplifying l = 9.049875621

Subproblem 2

l + 1 = -10.049875621 Simplifying l + 1 = -10.049875621 Reorder the terms: 1 + l = -10.049875621 Solving 1 + l = -10.049875621 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + l = -10.049875621 + -1 Combine like terms: 1 + -1 = 0 0 + l = -10.049875621 + -1 l = -10.049875621 + -1 Combine like terms: -10.049875621 + -1 = -11.049875621 l = -11.049875621 Simplifying l = -11.049875621

Solution

The solution to the problem is based on the solutions from the subproblems. l = {9.049875621, -11.049875621}

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