-120+3n+n^2=0

Simple and best practice solution for -120+3n+n^2=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 -120+3n+n^2=0 equation:


Simplifying
-120 + 3n + n2 = 0

Solving
-120 + 3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 3n + 120 + n2 = 0 + 120

Reorder the terms:
-120 + 120 + 3n + n2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 3n + n2 = 0 + 120
3n + n2 = 0 + 120

Combine like terms: 0 + 120 = 120
3n + n2 = 120

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 = 120 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 120 + 2.25

Combine like terms: 120 + 2.25 = 122.25
2.25 + 3n + n2 = 122.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(n + 1.5) equal to 11.056672194 and -11.056672194.

Subproblem 1

n + 1.5 = 11.056672194 Simplifying n + 1.5 = 11.056672194 Reorder the terms: 1.5 + n = 11.056672194 Solving 1.5 + n = 11.056672194 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 = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 11.056672194 + -1.5 n = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 n = 9.556672194 Simplifying n = 9.556672194

Subproblem 2

n + 1.5 = -11.056672194 Simplifying n + 1.5 = -11.056672194 Reorder the terms: 1.5 + n = -11.056672194 Solving 1.5 + n = -11.056672194 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 = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -11.056672194 + -1.5 n = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 n = -12.556672194 Simplifying n = -12.556672194

Solution

The solution to the problem is based on the solutions from the subproblems. n = {9.556672194, -12.556672194}

See similar equations:

| 5x^4+16x^3-15x^2+8x+16=0 | | 7G=-11 | | 6(t+5)=-6 | | -8+5x=2x+16 | | -4x+100=20 | | 5x+[3(x+40)]=600 | | 1/3x1/3x1/13 | | -7+[(3-12)-(-2-7)]= | | 4=-4(j+1) | | -n^2+n^3*2-(20-n+8)= | | -6.8(4T+6)-1.2(3T-5)= | | 3n+1(n-6)=3n(n-5) | | 4x/11=4x/5-24 | | 3x+3(1-y)-y=-6 | | 3=8*12 | | 2(3x-2)=5-3x | | x/8=x/9-11 | | -x-5y=-30 | | 7(-9)2power= | | 90-8m+m^2=0 | | ln(x/400) | | 3x=2/7 | | 9+2(x-3)=8-3(x-2) | | (40x^2)+(333x)+65=0 | | 3-2(9-8)= | | 4x+7=7x-20 | | 8+n[4]=4 | | 1/4(3-2x)=12/8 | | 15x-17=-6x+14 | | -2P+2*(1-p)=3p+0*(1-q) | | 28b=33b | | 1/18x12/5 |

Equations solver categories