l^2+90l-27000=0

Simple and best practice solution for l^2+90l-27000=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^2+90l-27000=0 equation: 


Simplifying
l2 + 90l + -27000 = 0

Reorder the terms:
-27000 + 90l + l2 = 0

Solving
-27000 + 90l + l2 = 0

Solving for variable 'l'.

Begin completing the square.

Move the constant term to the right:

Add '27000' to each side of the equation.
-27000 + 90l + 27000 + l2 = 0 + 27000

Reorder the terms:
-27000 + 27000 + 90l + l2 = 0 + 27000

Combine like terms: -27000 + 27000 = 0
0 + 90l + l2 = 0 + 27000
90l + l2 = 0 + 27000

Combine like terms: 0 + 27000 = 27000
90l + l2 = 27000

The l term is 90l.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90l + 2025 + l2 = 27000 + 2025

Reorder the terms:
2025 + 90l + l2 = 27000 + 2025

Combine like terms: 27000 + 2025 = 29025
2025 + 90l + l2 = 29025

Factor a perfect square on the left side:
(l + 45)(l + 45) = 29025

Calculate the square root of the right side: 170.367250374

Break this problem into two subproblems by setting 
(l + 45) equal to 170.367250374 and -170.367250374.


Subproblem 1
l + 45 = 170.367250374

Simplifying
l + 45 = 170.367250374

Reorder the terms:
45 + l = 170.367250374

Solving
45 + l = 170.367250374

Solving for variable 'l'.

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

Add '-45' to each side of the equation.
45 + -45 + l = 170.367250374 + -45

Combine like terms: 45 + -45 = 0
0 + l = 170.367250374 + -45
l = 170.367250374 + -45

Combine like terms: 170.367250374 + -45 = 125.367250374
l = 125.367250374

Simplifying
l = 125.367250374


Subproblem 2
l + 45 = -170.367250374

Simplifying
l + 45 = -170.367250374

Reorder the terms:
45 + l = -170.367250374

Solving
45 + l = -170.367250374

Solving for variable 'l'.

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

Add '-45' to each side of the equation.
45 + -45 + l = -170.367250374 + -45

Combine like terms: 45 + -45 = 0
0 + l = -170.367250374 + -45
l = -170.367250374 + -45

Combine like terms: -170.367250374 + -45 = -215.367250374
l = -215.367250374

Simplifying
l = -215.367250374


Solution
The solution to the problem is based on the solutions
from the subproblems.
l = {125.367250374, -215.367250374}

See similar equations:

| -6x+10=4(2x+2) | | 6x-104=100 | | 7x+6x-1+90=180 | | 21=xy | | 1=2x^2 | | x+x+4+3x-9= | | 24a-6(8-4a)+52= | | w+4=18 | | ax+cy=b | | -4(2n+6)-12=14 | | 3x=5+6x | | 4(2)+-6m=-2 | | 2x^2+3x=84 | | 1+r^10=1.5 | | N^2-5n+12=0 | | -(19+2g)-57+4g= | | .6(x-6)=7.8 | | 3+0.5x^2=16-8x^2 | | 0=-4.9t^2+15t+20 | | 18-9b=2b+4 | | -35-7n=7(-7n+7) | | 5(x+5)+x=4(x+3)+4 | | 16w-15=5+12w | | (-36x^2+144x-60)=0 | | 11-2(8+30)=49 | | -7(x+1)-12=41+3 | | 84y^2+y-9=0 | | 3.6-2.4d=24 | | 8(x+3)+5(x+3)=7x-7 | | 9x+12y=3 | | X+15=3x+20 | | -7(x+1)-12=14+3 |

Equations solver categories