l*l+5l-75=0

Simple and best practice solution for l*l+5l-75=0 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+5l-75=0 equation: 


Simplifying
l * l + 5l + -75 = 0

Multiply l * l
l2 + 5l + -75 = 0

Reorder the terms:
-75 + 5l + l2 = 0

Solving
-75 + 5l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 5l + 75 + l2 = 0 + 75

Reorder the terms:
-75 + 75 + 5l + l2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 5l + l2 = 0 + 75
5l + l2 = 0 + 75

Combine like terms: 0 + 75 = 75
5l + l2 = 75

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 = 75 + 6.25

Reorder the terms:
6.25 + 5l + l2 = 75 + 6.25

Combine like terms: 75 + 6.25 = 81.25
6.25 + 5l + l2 = 81.25

Factor a perfect square on the left side:
(l + 2.5)(l + 2.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(l + 2.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
l + 2.5 = 9.013878189

Simplifying
l + 2.5 = 9.013878189

Reorder the terms:
2.5 + l = 9.013878189

Solving
2.5 + l = 9.013878189

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 = 9.013878189 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + l = 9.013878189 + -2.5
l = 9.013878189 + -2.5

Combine like terms: 9.013878189 + -2.5 = 6.513878189
l = 6.513878189

Simplifying
l = 6.513878189


Subproblem 2
l + 2.5 = -9.013878189

Simplifying
l + 2.5 = -9.013878189

Reorder the terms:
2.5 + l = -9.013878189

Solving
2.5 + l = -9.013878189

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 = -9.013878189 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + l = -9.013878189 + -2.5
l = -9.013878189 + -2.5

Combine like terms: -9.013878189 + -2.5 = -11.513878189
l = -11.513878189

Simplifying
l = -11.513878189


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {6.513878189, -11.513878189}

See similar equations:

| 107=5y+12 | | 20(3x-7)=100 | | 2w-9w=14 | | 144acd/30bcd | | 3cos(t)=π/2 | | px+2y+8=0 | | 1/2x1/2= | | 3[x-9]=30 | | x+3y-2z=-5 | | 123x^2-3457y^3-65z^3=4 | | 5x-45+xy-9y=5(x-9)(5+y) | | (15x-45)+(24x-96)-20=0 | | h*-7=-56 | | 15x-45+24x-96-20=0 | | (x^2)/4-4y^2=1 | | 976y=0 | | 3(x-2)=(-9) | | 2e=16 | | 39x-161=0 | | -4(x+6)-4=-4x+(-28) | | (c-d)+7=7 | | -a/4*14 | | 2c+2d=4 | | x^2y+xy^2=0 | | -2/3a-4=10 | | 2*(3x+1)-20=12x | | 5v-5=10+2v | | 4q=-3q | | 3p=6+2p | | 4(2x+4)+5(4x+3)= | | 8xy=2450 | | 3x+28=8x-12 |

Equations solver categories