n^2+3n-2000=0

Simple and best practice solution for n^2+3n-2000=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 n^2+3n-2000=0 equation: 


Simplifying
n2 + 3n + -2000 = 0

Reorder the terms:
-2000 + 3n + n2 = 0

Solving
-2000 + 3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '2000' to each side of the equation.
-2000 + 3n + 2000 + n2 = 0 + 2000

Reorder the terms:
-2000 + 2000 + 3n + n2 = 0 + 2000

Combine like terms: -2000 + 2000 = 0
0 + 3n + n2 = 0 + 2000
3n + n2 = 0 + 2000

Combine like terms: 0 + 2000 = 2000
3n + n2 = 2000

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 2000 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 2000 + 2.25

Combine like terms: 2000 + 2.25 = 2002.25
2.25 + 3n + n2 = 2002.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 2002.25

Calculate the square root of the right side: 44.746508244

Break this problem into two subproblems by setting 
(n + 1.5) equal to 44.746508244 and -44.746508244.


Subproblem 1
n + 1.5 = 44.746508244

Simplifying
n + 1.5 = 44.746508244

Reorder the terms:
1.5 + n = 44.746508244

Solving
1.5 + n = 44.746508244

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = 44.746508244 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = 44.746508244 + -1.5
n = 44.746508244 + -1.5

Combine like terms: 44.746508244 + -1.5 = 43.246508244
n = 43.246508244

Simplifying
n = 43.246508244


Subproblem 2
n + 1.5 = -44.746508244

Simplifying
n + 1.5 = -44.746508244

Reorder the terms:
1.5 + n = -44.746508244

Solving
1.5 + n = -44.746508244

Solving for variable 'n'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + n = -44.746508244 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + n = -44.746508244 + -1.5
n = -44.746508244 + -1.5

Combine like terms: -44.746508244 + -1.5 = -46.246508244
n = -46.246508244

Simplifying
n = -46.246508244


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {43.246508244, -46.246508244}

See similar equations:

| y/2-4=15 | | -9(x-1)=-7x+5 | | -5.4-6y-7.1-y=-6-12.3 | | 12(8-11x)+7x=-7x-(14x+8) | | 1/4x-y=3 | | -15/19p=-8 | | 1/6q=9 | | K-100=463 | | -8v-30=-2(v-3) | | 8y-6(0)=24 | | 3-4c=-81 | | -2(x+8)=-18 | | 8(0)-6x=24 | | 4(2+w)=3(7+w) | | (x+6)+(x+6)+x+x+2x=102 | | 4t=-15-5 | | 5n(9n+2)=0 | | -5(x-6)=-2x+39 | | 7x+7=9x-3x | | 46+5y=98.5 | | -3.2-3x-3.8-x=-3x-0.5 | | -5x+x^2-36=0 | | 2logb(x-4)=1 | | (4x+23)=(6x+-7) | | -3(x+3)+6=-3 | | 14-8x=20-8x-6 | | 29+t=49 | | 42x-19=55x-58 | | ((1/4)=((31/8)/x) | | 31+x=100 | | 3x-7/10=x-11 | | 21x-9=180 |

Equations solver categories