n^2-23=-8n

Simple and best practice solution for n^2-23=-8n 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^2-23=-8n equation:


Simplifying
n2 + -23 = -8n

Reorder the terms:
-23 + n2 = -8n

Solving
-23 + n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-23 + 8n + n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-23 + 8n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 8n + 23 + n2 = 0 + 23

Reorder the terms:
-23 + 23 + 8n + n2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 8n + n2 = 0 + 23
8n + n2 = 0 + 23

Combine like terms: 0 + 23 = 23
8n + n2 = 23

The n term is 8n.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8n + 16 + n2 = 23 + 16

Reorder the terms:
16 + 8n + n2 = 23 + 16

Combine like terms: 23 + 16 = 39
16 + 8n + n2 = 39

Factor a perfect square on the left side:
(n + 4)(n + 4) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(n + 4) equal to 6.244997998 and -6.244997998.

Subproblem 1

n + 4 = 6.244997998 Simplifying n + 4 = 6.244997998 Reorder the terms: 4 + n = 6.244997998 Solving 4 + n = 6.244997998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = 6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + n = 6.244997998 + -4 n = 6.244997998 + -4 Combine like terms: 6.244997998 + -4 = 2.244997998 n = 2.244997998 Simplifying n = 2.244997998

Subproblem 2

n + 4 = -6.244997998 Simplifying n + 4 = -6.244997998 Reorder the terms: 4 + n = -6.244997998 Solving 4 + n = -6.244997998 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + n = -6.244997998 + -4 Combine like terms: 4 + -4 = 0 0 + n = -6.244997998 + -4 n = -6.244997998 + -4 Combine like terms: -6.244997998 + -4 = -10.244997998 n = -10.244997998 Simplifying n = -10.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.244997998, -10.244997998}

See similar equations:

| 4y=z-3 | | -7(-2n-4)=5(n-3)+-6 | | -2(x+6)+6x=5(x-5)+30 | | 2-6(8q-3)= | | 15/12-1/4 | | -7(-2n-4)=5(n+-3)+-6 | | d/-3=-42 | | 4(n+2)-4(3n-5)=-28 | | X-2+2x+4=x | | -1/8-1/7 | | 4c-2=2(2c-1) | | 1.4r+5=30 | | 15n^2-24=9n | | -7(-2n-4)=5(n-3)-6 | | 1.4r+5= | | 1.4r+30=5 | | 6x-8=-3x+15 | | 5+35=1.4r | | 32(3.14)t=64(3.14) | | 35+1.4r=5 | | 5+1.4r=35 | | (x+5)=y+2y | | 5+1.4r=30 | | -2+1=x+5 | | 32(3.14)=64(3.14) | | 3.5=5X-3 | | 7y-9-2y+5=0 | | 38/50 | | 10-(4-b)=b-6 | | y=16x+13 | | 4x+10=-3-3x | | (X-2)(x-2)=11x+4 |

Equations solver categories