n^2+8n+8=0

Simple and best practice solution for n^2+8n+8=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+8n+8=0 equation: 


Simplifying
n2 + 8n + 8 = 0

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

Solving
8 + 8n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -8 + 16

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

Combine like terms: -8 + 16 = 8
16 + 8n + n2 = 8

Factor a perfect square on the left side:
(n + 4)(n + 4) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(n + 4) equal to 2.828427125 and -2.828427125.


Subproblem 1
n + 4 = 2.828427125

Simplifying
n + 4 = 2.828427125

Reorder the terms:
4 + n = 2.828427125

Solving
4 + n = 2.828427125

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 = 2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + n = 2.828427125 + -4
n = 2.828427125 + -4

Combine like terms: 2.828427125 + -4 = -1.171572875
n = -1.171572875

Simplifying
n = -1.171572875


Subproblem 2
n + 4 = -2.828427125

Simplifying
n + 4 = -2.828427125

Reorder the terms:
4 + n = -2.828427125

Solving
4 + n = -2.828427125

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 = -2.828427125 + -4

Combine like terms: 4 + -4 = 0
0 + n = -2.828427125 + -4
n = -2.828427125 + -4

Combine like terms: -2.828427125 + -4 = -6.828427125
n = -6.828427125

Simplifying
n = -6.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-1.171572875, -6.828427125}

See similar equations:

| y=-3x^2-42x-144 | | 50(2-0.5c)-70=20-5c | | -2xy-2xy= | | 2/5=h+8/h+26 | | 3x^2-22x+50=0 | | 5+7(x-9)=4x-16 | | 6(x-3)=2(3x+5) | | 3x+2/4=3 | | 5x-11/3y=29 | | y+2D=t | | 6x+14=-49-3x | | 5.25a-2(3a+1.25)=a+1 | | 4x-5/3y=-9 | | 9y+3=4+13 | | 8+5x=8+x | | 9(2x-1)+2(3x+4)=20x+3 | | 4/5*m=1 | | 3-3x=3(2x-2) | | 4.6w+0.1=55.39 | | 12.5x^5/3 | | (x-3)(y+6)=s+78 | | 4.5x+2x=0 | | 3j=2.5 | | -20r+6r^2+2r^3=0 | | 4p+5q=7 | | -7+6=27 | | lnx=.0000000955 | | -7u-8u=-4-18 | | 6/21=10/x | | 3b+8=20 | | -92+9(-8+9)+14= | | ax-bx=d |

Equations solver categories