n^2+6n-1000=0

Simple and best practice solution for n^2+6n-1000=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+6n-1000=0 equation:


Simplifying
n2 + 6n + -1000 = 0

Reorder the terms:
-1000 + 6n + n2 = 0

Solving
-1000 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + 6n + 1000 + n2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + 6n + n2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + 6n + n2 = 0 + 1000
6n + n2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
6n + n2 = 1000

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = 1000 + 9

Reorder the terms:
9 + 6n + n2 = 1000 + 9

Combine like terms: 1000 + 9 = 1009
9 + 6n + n2 = 1009

Factor a perfect square on the left side:
(n + 3)(n + 3) = 1009

Calculate the square root of the right side: 31.764760349

Break this problem into two subproblems by setting 
(n + 3) equal to 31.764760349 and -31.764760349.

Subproblem 1

n + 3 = 31.764760349 Simplifying n + 3 = 31.764760349 Reorder the terms: 3 + n = 31.764760349 Solving 3 + n = 31.764760349 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 31.764760349 + -3 Combine like terms: 3 + -3 = 0 0 + n = 31.764760349 + -3 n = 31.764760349 + -3 Combine like terms: 31.764760349 + -3 = 28.764760349 n = 28.764760349 Simplifying n = 28.764760349

Subproblem 2

n + 3 = -31.764760349 Simplifying n + 3 = -31.764760349 Reorder the terms: 3 + n = -31.764760349 Solving 3 + n = -31.764760349 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -31.764760349 + -3 Combine like terms: 3 + -3 = 0 0 + n = -31.764760349 + -3 n = -31.764760349 + -3 Combine like terms: -31.764760349 + -3 = -34.764760349 n = -34.764760349 Simplifying n = -34.764760349

Solution

The solution to the problem is based on the solutions from the subproblems. n = {28.764760349, -34.764760349}

See similar equations:

| 8(3x-6)+4(-5-1)=8 | | 16+4x=84 | | 62.70=11.6t+97.5 | | f(x)=5x^2+10x | | 7x+9=75whatisx | | 35=5(-9+n) | | 9x+9=-72 | | 5x+4x=4+9 | | 5b-4c+2a-6a+4b-10= | | 2(x+2)=(x+4) | | 4x-x^3=16 | | 10z-8+9z+5r+11= | | 6x-8x+5x-2= | | y/3-1,5=11,5 | | 6x-8x+5r+11= | | 10x-17=9x+11 | | 3s+5-12+15s= | | 12x-84=6x-12 | | 20f-25f+6-4= | | 6k+2(-3k-4)=0 | | 7+c+2c-5= | | 2x-6=21-x | | 5p-8b+14p= | | (9a*a)-(b*b)-4b=4 | | (9a*a)-(b*b)-4b-4=0 | | 9g+5a-6a-8g= | | 5x+4=62 | | 12r+4r-8c= | | 5/12*12/8 | | 7a-6=9a-11 | | =20-2x*20-2x | | 3x-5+2x+3=6x+5 |

Equations solver categories