12n^2=-n+16

Simple and best practice solution for 12n^2=-n+16 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 12n^2=-n+16 equation:


Simplifying
12n2 = -1n + 16

Reorder the terms:
12n2 = 16 + -1n

Solving
12n2 = 16 + -1n

Solving for variable 'n'.

Reorder the terms:
-16 + n + 12n2 = 16 + -1n + -16 + n

Reorder the terms:
-16 + n + 12n2 = 16 + -16 + -1n + n

Combine like terms: 16 + -16 = 0
-16 + n + 12n2 = 0 + -1n + n
-16 + n + 12n2 = -1n + n

Combine like terms: -1n + n = 0
-16 + n + 12n2 = 0

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

Divide each side by '12'.
-1.333333333 + 0.08333333333n + n2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 0.08333333333n + 1.333333333 + n2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 0.08333333333n + n2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 0.08333333333n + n2 = 0 + 1.333333333
0.08333333333n + n2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
0.08333333333n + n2 = 1.333333333

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.08333333333n + 0.25 + n2 = 1.333333333 + 0.25

Reorder the terms:
0.25 + 0.08333333333n + n2 = 1.333333333 + 0.25

Combine like terms: 1.333333333 + 0.25 = 1.583333333
0.25 + 0.08333333333n + n2 = 1.583333333

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 1.583333333

Calculate the square root of the right side: 1.258305739

Break this problem into two subproblems by setting 
(n + 0.5) equal to 1.258305739 and -1.258305739.

Subproblem 1

n + 0.5 = 1.258305739 Simplifying n + 0.5 = 1.258305739 Reorder the terms: 0.5 + n = 1.258305739 Solving 0.5 + n = 1.258305739 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 1.258305739 + -0.5 n = 1.258305739 + -0.5 Combine like terms: 1.258305739 + -0.5 = 0.758305739 n = 0.758305739 Simplifying n = 0.758305739

Subproblem 2

n + 0.5 = -1.258305739 Simplifying n + 0.5 = -1.258305739 Reorder the terms: 0.5 + n = -1.258305739 Solving 0.5 + n = -1.258305739 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -1.258305739 + -0.5 n = -1.258305739 + -0.5 Combine like terms: -1.258305739 + -0.5 = -1.758305739 n = -1.758305739 Simplifying n = -1.758305739

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.758305739, -1.758305739}

See similar equations:

| 3j-J+3j-3j=14 | | 26-7x=15 | | 16-x*5=-4 | | 17p+3p+3p+p-19p=15 | | 3(x-3)+8=6x-3(1+x) | | 1x-6=4 | | 4(9v+5)=-23+6v | | 2c+8c=20 | | 2senx+cosx=1 | | X+128=123 | | f^2+8f+7=0 | | (2x-5)+(5X+15)(4x-15)=180 | | 9j-7j=18 | | -7x+2(x+4)=23 | | ax=33is(6) | | -7x+2(x-4)=23 | | 11-5x=-10x | | 9x-16=x+5 | | 2x^2-5x=16 | | 17g-13g=4 | | 0.8x-3.3=9.3 | | -3(4+5n)=108 | | 2x-28=x | | 32=4y+8(y-8) | | Sin45=x/16 | | k^2-143=2k | | 7(7p+3)=119 | | 4x-87=2x-23 | | 2x-30=2x | | 13x+8=12x+17 | | ax=30is(6) | | 7(4x-3)+9=28x-12 |

Equations solver categories