l(l+4)=100

Simple and best practice solution for l(l+4)=100 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for l(l+4)=100 equation: 


Simplifying
l(l + 4) = 100

Reorder the terms:
l(4 + l) = 100
(4 * l + l * l) = 100
(4l + l2) = 100

Solving
4l + l2 = 100

Solving for variable 'l'.

Reorder the terms:
-100 + 4l + l2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 4l + l2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 4l + 100 + l2 = 0 + 100

Reorder the terms:
-100 + 100 + 4l + l2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 4l + l2 = 0 + 100
4l + l2 = 0 + 100

Combine like terms: 0 + 100 = 100
4l + l2 = 100

The l term is 4l.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4l + 4 + l2 = 100 + 4

Reorder the terms:
4 + 4l + l2 = 100 + 4

Combine like terms: 100 + 4 = 104
4 + 4l + l2 = 104

Factor a perfect square on the left side:
(l + 2)(l + 2) = 104

Calculate the square root of the right side: 10.198039027

Break this problem into two subproblems by setting 
(l + 2) equal to 10.198039027 and -10.198039027.


Subproblem 1
l + 2 = 10.198039027

Simplifying
l + 2 = 10.198039027

Reorder the terms:
2 + l = 10.198039027

Solving
2 + l = 10.198039027

Solving for variable 'l'.

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

Add '-2' to each side of the equation.
2 + -2 + l = 10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + l = 10.198039027 + -2
l = 10.198039027 + -2

Combine like terms: 10.198039027 + -2 = 8.198039027
l = 8.198039027

Simplifying
l = 8.198039027


Subproblem 2
l + 2 = -10.198039027

Simplifying
l + 2 = -10.198039027

Reorder the terms:
2 + l = -10.198039027

Solving
2 + l = -10.198039027

Solving for variable 'l'.

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

Add '-2' to each side of the equation.
2 + -2 + l = -10.198039027 + -2

Combine like terms: 2 + -2 = 0
0 + l = -10.198039027 + -2
l = -10.198039027 + -2

Combine like terms: -10.198039027 + -2 = -12.198039027
l = -12.198039027

Simplifying
l = -12.198039027


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {8.198039027, -12.198039027}

See similar equations:

| (3t-4)(3t-4)=0 | | l+l+4=100 | | (3x+7)/4+(x+53)/7=12 | | .09x+.25(10-x)=.15(10) | | 3a^2=192 | | -16(3t+-4)+55=0 | | 2(x-8)=3x+3 | | 9x-2x-28=14 | | -4(t-5)+8t=9t-9 | | 28/16=x-8/20 | | D/30+1=4 | | 7b-4=-9 | | -2x+3= | | 25=5q-50 | | 4xy^2-8= | | 2t=3t+1 | | 62=3c+8 | | d-257x=8328 | | 3r^2-3r-15= | | x/6-18=0 | | (x^2)-4x-32= | | 3a+7=4a+9 | | 11x-(7x-2)=10 | | (5a+6)=2(3a+8) | | 5x^2-25x=30 | | x^2+25x-224=0 | | 12cos(x)-6=0 | | -39=-6+3(x-3) | | 14+3n=7b-7.4 | | (-3/4x+24)+2=-1/x+6 | | 450-3x=300 | | -2x+6=-8 |

Equations solver categories