n^2-12=3n

Simple and best practice solution for n^2-12=3n 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^2-12=3n equation:


Simplifying
n2 + -12 = 3n

Reorder the terms:
-12 + n2 = 3n

Solving
-12 + n2 = 3n

Solving for variable 'n'.

Reorder the terms:
-12 + -3n + n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-12 + -3n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -3n + 12 + n2 = 0 + 12

Reorder the terms:
-12 + 12 + -3n + n2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -3n + n2 = 0 + 12
-3n + n2 = 0 + 12

Combine like terms: 0 + 12 = 12
-3n + n2 = 12

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 12 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 12 + 2.25

Combine like terms: 12 + 2.25 = 14.25
2.25 + -3n + n2 = 14.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(n + -1.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

n + -1.5 = 3.774917218 Simplifying n + -1.5 = 3.774917218 Reorder the terms: -1.5 + n = 3.774917218 Solving -1.5 + n = 3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 3.774917218 + 1.5 n = 3.774917218 + 1.5 Combine like terms: 3.774917218 + 1.5 = 5.274917218 n = 5.274917218 Simplifying n = 5.274917218

Subproblem 2

n + -1.5 = -3.774917218 Simplifying n + -1.5 = -3.774917218 Reorder the terms: -1.5 + n = -3.774917218 Solving -1.5 + n = -3.774917218 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -3.774917218 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -3.774917218 + 1.5 n = -3.774917218 + 1.5 Combine like terms: -3.774917218 + 1.5 = -2.274917218 n = -2.274917218 Simplifying n = -2.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.274917218, -2.274917218}

See similar equations:

| 8x+7(2-3)=-6(2x+5) | | 12=1/3(-12n+30) | | (4k-1)(k-4)=0 | | Z=px+qy+p^2q^2 | | 15+y=8 | | 17-2x+4x=35 | | 5x-7y=-20 | | -x^3+15x^2+600x=0 | | 28x^3-22x^2-16x+88=0 | | 8x-7=2x+14 | | 2xy-y^2=3 | | 3d^2+3D-10=0 | | x^3-15x^2-600x=0 | | 6[8+x]=30 | | . 2x+12=4x | | x^2+15x+600=0 | | 2x-33=44 | | 9x^4-12x^2-4=0 | | -5(w-1)-(5w-9)=-11w | | -80000x+-2000000=-4200000 | | 5m^2-32m+12=0 | | 5m^2-32m+13=0 | | 60x-30y=120 | | 9(w+8)=8w-7 | | c^2+3c=26.2 | | -80000x+-2000000=-3600000 | | 3n^2+5n=4 | | 5m^2-33m+13=0 | | z^2+2(1-2i)z+2=0 | | -80000+-2000000=-3600000 | | 4w^2-4w=3 | | 4x+2(5+3x)=260 |

Equations solver categories