3n^2-n-4=2

Simple and best practice solution for 3n^2-n-4=2 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 3n^2-n-4=2 equation:


Simplifying
3n2 + -1n + -4 = 2

Reorder the terms:
-4 + -1n + 3n2 = 2

Solving
-4 + -1n + 3n2 = 2

Solving for variable 'n'.

Reorder the terms:
-4 + -2 + -1n + 3n2 = 2 + -2

Combine like terms: -4 + -2 = -6
-6 + -1n + 3n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-6 + -1n + 3n2 = 0

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

Divide each side by '3'.
-2 + -0.3333333333n + n2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.3333333333n + 2 + n2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.3333333333n + n2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.3333333333n + n2 = 0 + 2
-0.3333333333n + n2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.3333333333n + n2 = 2

The n term is -0.3333333333n.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333n + 0.02777777779 + n2 = 2 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333n + n2 = 2 + 0.02777777779

Combine like terms: 2 + 0.02777777779 = 2.02777777779
0.02777777779 + -0.3333333333n + n2 = 2.02777777779

Factor a perfect square on the left side:
(n + -0.1666666667)(n + -0.1666666667) = 2.02777777779

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(n + -0.1666666667) equal to 1.424000624 and -1.424000624.

Subproblem 1

n + -0.1666666667 = 1.424000624 Simplifying n + -0.1666666667 = 1.424000624 Reorder the terms: -0.1666666667 + n = 1.424000624 Solving -0.1666666667 + n = 1.424000624 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = 1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = 1.424000624 + 0.1666666667 n = 1.424000624 + 0.1666666667 Combine like terms: 1.424000624 + 0.1666666667 = 1.5906672907 n = 1.5906672907 Simplifying n = 1.5906672907

Subproblem 2

n + -0.1666666667 = -1.424000624 Simplifying n + -0.1666666667 = -1.424000624 Reorder the terms: -0.1666666667 + n = -1.424000624 Solving -0.1666666667 + n = -1.424000624 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + n = -1.424000624 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + n = -1.424000624 + 0.1666666667 n = -1.424000624 + 0.1666666667 Combine like terms: -1.424000624 + 0.1666666667 = -1.2573339573 n = -1.2573339573 Simplifying n = -1.2573339573

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.5906672907, -1.2573339573}

See similar equations:

| (2x-5)(5x+2)=0 | | .40x-8=20+.75x | | x^2+4x-71=0 | | z^2+15z+56=0 | | (9x+2)(2(x)(x)-5x-3)=0 | | 3x+20=-4 | | -x^2+8x+37=0 | | 4(x)(x)-25=0 | | 7x^2+0x-3=0 | | 4(t-2)+4t=(2t+4)-10 | | x^2+20x-10=0 | | 7x-x+2x=48 | | -5y-10=8y+16 | | 3x^2-18x-20=0 | | 8(x-8)=3 | | x^3y^3-27= | | b^2-8b+4=0 | | -6x-12=7y | | 16(x)(x)(x)-x=0 | | -7y=-6x-12 | | 7x-11y=13 | | 8x-3y=24 | | (8x+5)(2x^2-17x-9)=0 | | -54=-6x | | -9x+5m+7x-2m= | | (7x+4)(x-3)=0 | | 5(x-8)=9 | | (x)(x)-3x=40 | | (x)(x)+59x=0 | | 2x=5x+4 | | a+1+a-t= | | (x)(x)-13x+40=0 |

Equations solver categories