2l^2+14l-123=0

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Solution for 2l^2+14l-123=0 equation:


Simplifying
2l2 + 14l + -123 = 0

Reorder the terms:
-123 + 14l + 2l2 = 0

Solving
-123 + 14l + 2l2 = 0

Solving for variable 'l'.

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

Divide each side by '2'.
-61.5 + 7l + l2 = 0

Move the constant term to the right:

Add '61.5' to each side of the equation.
-61.5 + 7l + 61.5 + l2 = 0 + 61.5

Reorder the terms:
-61.5 + 61.5 + 7l + l2 = 0 + 61.5

Combine like terms: -61.5 + 61.5 = 0.0
0.0 + 7l + l2 = 0 + 61.5
7l + l2 = 0 + 61.5

Combine like terms: 0 + 61.5 = 61.5
7l + l2 = 61.5

The l term is 7l.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7l + 12.25 + l2 = 61.5 + 12.25

Reorder the terms:
12.25 + 7l + l2 = 61.5 + 12.25

Combine like terms: 61.5 + 12.25 = 73.75
12.25 + 7l + l2 = 73.75

Factor a perfect square on the left side:
(l + 3.5)(l + 3.5) = 73.75

Calculate the square root of the right side: 8.587782019

Break this problem into two subproblems by setting 
(l + 3.5) equal to 8.587782019 and -8.587782019.

Subproblem 1

l + 3.5 = 8.587782019 Simplifying l + 3.5 = 8.587782019 Reorder the terms: 3.5 + l = 8.587782019 Solving 3.5 + l = 8.587782019 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + l = 8.587782019 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + l = 8.587782019 + -3.5 l = 8.587782019 + -3.5 Combine like terms: 8.587782019 + -3.5 = 5.087782019 l = 5.087782019 Simplifying l = 5.087782019

Subproblem 2

l + 3.5 = -8.587782019 Simplifying l + 3.5 = -8.587782019 Reorder the terms: 3.5 + l = -8.587782019 Solving 3.5 + l = -8.587782019 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + l = -8.587782019 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + l = -8.587782019 + -3.5 l = -8.587782019 + -3.5 Combine like terms: -8.587782019 + -3.5 = -12.087782019 l = -12.087782019 Simplifying l = -12.087782019

Solution

The solution to the problem is based on the solutions from the subproblems. l = {5.087782019, -12.087782019}

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