n^2+30n+120=0

Simple and best practice solution for n^2+30n+120=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 n^2+30n+120=0 equation:


Simplifying
n2 + 30n + 120 = 0

Reorder the terms:
120 + 30n + n2 = 0

Solving
120 + 30n + 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 + 30n + -120 + n2 = 0 + -120

Reorder the terms:
120 + -120 + 30n + n2 = 0 + -120

Combine like terms: 120 + -120 = 0
0 + 30n + n2 = 0 + -120
30n + n2 = 0 + -120

Combine like terms: 0 + -120 = -120
30n + n2 = -120

The n term is 30n.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30n + 225 + n2 = -120 + 225

Reorder the terms:
225 + 30n + n2 = -120 + 225

Combine like terms: -120 + 225 = 105
225 + 30n + n2 = 105

Factor a perfect square on the left side:
(n + 15)(n + 15) = 105

Calculate the square root of the right side: 10.246950766

Break this problem into two subproblems by setting 
(n + 15) equal to 10.246950766 and -10.246950766.

Subproblem 1

n + 15 = 10.246950766 Simplifying n + 15 = 10.246950766 Reorder the terms: 15 + n = 10.246950766 Solving 15 + n = 10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + n = 10.246950766 + -15 Combine like terms: 15 + -15 = 0 0 + n = 10.246950766 + -15 n = 10.246950766 + -15 Combine like terms: 10.246950766 + -15 = -4.753049234 n = -4.753049234 Simplifying n = -4.753049234

Subproblem 2

n + 15 = -10.246950766 Simplifying n + 15 = -10.246950766 Reorder the terms: 15 + n = -10.246950766 Solving 15 + n = -10.246950766 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + n = -10.246950766 + -15 Combine like terms: 15 + -15 = 0 0 + n = -10.246950766 + -15 n = -10.246950766 + -15 Combine like terms: -10.246950766 + -15 = -25.246950766 n = -25.246950766 Simplifying n = -25.246950766

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-4.753049234, -25.246950766}

See similar equations:

| 7x+35=11x+35 | | (-4x^2+9x)+(14x^2-2x-3)= | | X/11+4=-8 | | 2.9(x+3.1)=6.9 | | 5x-4(9-3x)=-2 | | x-6=3y | | 18x^2-45=0 | | -4.9t^2+20t=0 | | 19=h/3-8 | | 1/5(x-6)=5x-4(x-1)+38/5 | | 5+2s=48 | | 5a+2=48 | | 19=9/3-8 | | -2x+6=-12x-44 | | 1/5(x-5)=3x-2(x-1)-21/5 | | 5=3n+8/4 | | 1/5(x+2)=3x-4(3-x)-8 | | 21-[2x-4]=13 | | [-3x+7]=8 | | -10n+4=-6n-8 | | -14=n/3 | | .8w-.5w+.2w=5 | | -9x-8=-4x+7 | | 5-3(x+4)=-8x+4(x+3) | | 4x^2-7x=2 | | 36x^3-24x^2+4x=0 | | 3x+4(x-6)-3(x-7)= | | 23+26= | | x+2=11x+17 | | 4-(9-3x)=7 | | 2/5(4x+11)=4(1-2x)+10 | | -4/5x=2/5 |

Equations solver categories