8n^2+8=6-9n

Simple and best practice solution for 8n^2+8=6-9n 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 8n^2+8=6-9n equation:


Simplifying
8n2 + 8 = 6 + -9n

Reorder the terms:
8 + 8n2 = 6 + -9n

Solving
8 + 8n2 = 6 + -9n

Solving for variable 'n'.

Reorder the terms:
8 + -6 + 9n + 8n2 = 6 + -9n + -6 + 9n

Combine like terms: 8 + -6 = 2
2 + 9n + 8n2 = 6 + -9n + -6 + 9n

Reorder the terms:
2 + 9n + 8n2 = 6 + -6 + -9n + 9n

Combine like terms: 6 + -6 = 0
2 + 9n + 8n2 = 0 + -9n + 9n
2 + 9n + 8n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
2 + 9n + 8n2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.25 + 1.125n + n2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 1.125n + -0.25 + n2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 1.125n + n2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 1.125n + n2 = 0 + -0.25
1.125n + n2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
1.125n + n2 = -0.25

The n term is 1.125n.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125n + 0.31640625 + n2 = -0.25 + 0.31640625

Reorder the terms:
0.31640625 + 1.125n + n2 = -0.25 + 0.31640625

Combine like terms: -0.25 + 0.31640625 = 0.06640625
0.31640625 + 1.125n + n2 = 0.06640625

Factor a perfect square on the left side:
(n + 0.5625)(n + 0.5625) = 0.06640625

Calculate the square root of the right side: 0.257694102

Break this problem into two subproblems by setting 
(n + 0.5625) equal to 0.257694102 and -0.257694102.

Subproblem 1

n + 0.5625 = 0.257694102 Simplifying n + 0.5625 = 0.257694102 Reorder the terms: 0.5625 + n = 0.257694102 Solving 0.5625 + n = 0.257694102 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + n = 0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + n = 0.257694102 + -0.5625 n = 0.257694102 + -0.5625 Combine like terms: 0.257694102 + -0.5625 = -0.304805898 n = -0.304805898 Simplifying n = -0.304805898

Subproblem 2

n + 0.5625 = -0.257694102 Simplifying n + 0.5625 = -0.257694102 Reorder the terms: 0.5625 + n = -0.257694102 Solving 0.5625 + n = -0.257694102 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + n = -0.257694102 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + n = -0.257694102 + -0.5625 n = -0.257694102 + -0.5625 Combine like terms: -0.257694102 + -0.5625 = -0.820194102 n = -0.820194102 Simplifying n = -0.820194102

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.304805898, -0.820194102}

See similar equations:

| 10x+65=3x | | 8n^2=6-9n | | 3z=2.1+1.5 | | -72=-8x | | y(2)+30=14y | | 57=12+3r | | -3z=36 | | -8p=56 | | 6w-18w=96 | | 2*(n-3)=4n+1 | | 6.9x=35.19 | | 3x+28=20 | | 18=-z+6 | | 2x^2-20x+18=0 | | 12x+3y=21 | | ln(2x-3)-ln(x)=6 | | 3(n+9)=33 | | 4x+8-2x=20 | | 100m^2-49n^2=0 | | 2f-9=14f+11 | | -(-2x)=(-33) | | 5x-3y=11 | | ln(3x+2)-lnx=6 | | 30=9x-3 | | 3(m+9)-31= | | 5x+2=4(x-4)+5 | | 0.4(a-10)=0.8(5a+4) | | 2c+7.5=6.2-6b | | .29x^2-.18=.63x | | 3(b-8)=18 | | x(10-3x)+6=x(4x-9) | | 6(c+1)c=6 |

Equations solver categories