3n^2+11n+4=0

Simple and best practice solution for 3n^2+11n+4=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 3n^2+11n+4=0 equation: 


Simplifying
3n2 + 11n + 4 = 0

Reorder the terms:
4 + 11n + 3n2 = 0

Solving
4 + 11n + 3n2 = 0

Solving for variable 'n'.

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

Divide each side by '3'.
1.333333333 + 3.666666667n + n2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3.666666667n + -1.333333333 + n2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3.666666667n + n2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3.666666667n + n2 = 0 + -1.333333333
3.666666667n + n2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3.666666667n + n2 = -1.333333333

The n term is 3.666666667n.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667n + 3.361111114 + n2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667n + n2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + 3.666666667n + n2 = 2.027777781

Factor a perfect square on the left side:
(n + 1.833333334)(n + 1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(n + 1.833333334) equal to 1.424000625 and -1.424000625.


Subproblem 1
n + 1.833333334 = 1.424000625

Simplifying
n + 1.833333334 = 1.424000625

Reorder the terms:
1.833333334 + n = 1.424000625

Solving
1.833333334 + n = 1.424000625

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + n = 1.424000625 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + n = 1.424000625 + -1.833333334
n = 1.424000625 + -1.833333334

Combine like terms: 1.424000625 + -1.833333334 = -0.409332709
n = -0.409332709

Simplifying
n = -0.409332709


Subproblem 2
n + 1.833333334 = -1.424000625

Simplifying
n + 1.833333334 = -1.424000625

Reorder the terms:
1.833333334 + n = -1.424000625

Solving
1.833333334 + n = -1.424000625

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + n = -1.424000625 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + n = -1.424000625 + -1.833333334
n = -1.424000625 + -1.833333334

Combine like terms: -1.424000625 + -1.833333334 = -3.257333959
n = -3.257333959

Simplifying
n = -3.257333959


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.409332709, -3.257333959}

See similar equations:

| 7p+2=5p-4 | | 2sin^2x+sing=0 | | 5*x+9=-16 | | 2x+11=3X+3 | | 7x-11=5x+2 | | s*4-40=8 | | 5(2x+1)-3(x-3)= | | 7-3G=15 | | 24-8x=7x-42 | | 2/3x^1.5=3x^-2 | | 3(x+4)+4(x-2)= | | 31x+52y=8888 | | 70+3x+20=180 | | ln(x/8)=x-2 | | 4x*9x+6=90 | | 130+95+x=360 | | 130+35+x=360 | | f/4=7 | | 4x-8=7x+11 | | 9184=s*2296 | | 120/X=1500/300 | | x+25=5x-55 | | 7y+3d-4y+2d= | | 3y+5d= | | 7s+45=122 | | PQR=(2x+30) | | .50x+.75=x-.25 | | 56x=y^2 | | 30+B=b*b | | -8-7x-7-[2-(2X-4)]=4-[X-(4-5X)] | | A+B=b*b | | 24-8x=7x-6 |

Equations solver categories