2n^2+2n-n^2-6=0

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


Simplifying
2n2 + 2n + -1n2 + -6 = 0

Reorder the terms:
-6 + 2n + 2n2 + -1n2 = 0

Combine like terms: 2n2 + -1n2 = 1n2
-6 + 2n + 1n2 = 0

Solving
-6 + 2n + 1n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 2n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + 2n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2n + n2 = 0 + 6
2n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
2n + n2 = 6

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 6 + 1

Reorder the terms:
1 + 2n + n2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + 2n + n2 = 7

Factor a perfect square on the left side:
(n + 1)(n + 1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(n + 1) equal to 2.645751311 and -2.645751311.

Subproblem 1

n + 1 = 2.645751311 Simplifying n + 1 = 2.645751311 Reorder the terms: 1 + n = 2.645751311 Solving 1 + n = 2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = 2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + n = 2.645751311 + -1 n = 2.645751311 + -1 Combine like terms: 2.645751311 + -1 = 1.645751311 n = 1.645751311 Simplifying n = 1.645751311

Subproblem 2

n + 1 = -2.645751311 Simplifying n + 1 = -2.645751311 Reorder the terms: 1 + n = -2.645751311 Solving 1 + n = -2.645751311 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + n = -2.645751311 + -1 Combine like terms: 1 + -1 = 0 0 + n = -2.645751311 + -1 n = -2.645751311 + -1 Combine like terms: -2.645751311 + -1 = -3.645751311 n = -3.645751311 Simplifying n = -3.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.645751311, -3.645751311}

See similar equations:

| 5(7+x)=30 | | 6x+4=4x+13 | | =100-75z-50z^2 | | 2x^4-9x^2+7= | | 0=-2x^3+6x^2-3 | | 5x^2-8n+2=0 | | Y=15X+8 | | 0.5-x=0.75 | | (6a)(7b)= | | 4x-5y=h | | a+a+7+7=50 | | 14+4(y-5)=6-2y | | 18-k=90 | | 6x+9=5x-29 | | 5-3x=-x | | =12x^2+16x-8 | | 5k+3k=9+3 | | cya+w=9 | | 2(-4)-5y-2= | | 8x-3=4x-7 | | =10r^3-35r | | 21x-11=5(4x-4)-9 | | -2e-4=-1-e | | 0.19y+0.03(y+7000)=1530 | | 8x+28=140 | | 4+3+b=26 | | 4a+4b=34 | | 0.7x-0.2=0.6x+5 | | (9x+2)-(2x-5)= | | 6[3-(-4x-2)]=72x+54 | | n*(-5x)=1 | | 6+x+x=385 |

Equations solver categories