N^2+N-48=0

Simple and best practice solution for N^2+N-48=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+N-48=0 equation: 


Simplifying
N2 + N + -48 = 0

Reorder the terms:
-48 + N + N2 = 0

Solving
-48 + N + N2 = 0

Solving for variable 'N'.

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + N + 48 + N2 = 0 + 48

Reorder the terms:
-48 + 48 + N + N2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + N + N2 = 0 + 48
N + N2 = 0 + 48

Combine like terms: 0 + 48 = 48
N + N2 = 48

The N term is N.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
N + 0.25 + N2 = 48 + 0.25

Reorder the terms:
0.25 + N + N2 = 48 + 0.25

Combine like terms: 48 + 0.25 = 48.25
0.25 + N + N2 = 48.25

Factor a perfect square on the left side:
(N + 0.5)(N + 0.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(N + 0.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
N + 0.5 = 6.946221995

Simplifying
N + 0.5 = 6.946221995

Reorder the terms:
0.5 + N = 6.946221995

Solving
0.5 + N = 6.946221995

Solving for variable 'N'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + N = 6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + N = 6.946221995 + -0.5
N = 6.946221995 + -0.5

Combine like terms: 6.946221995 + -0.5 = 6.446221995
N = 6.446221995

Simplifying
N = 6.446221995


Subproblem 2
N + 0.5 = -6.946221995

Simplifying
N + 0.5 = -6.946221995

Reorder the terms:
0.5 + N = -6.946221995

Solving
0.5 + N = -6.946221995

Solving for variable 'N'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + N = -6.946221995 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + N = -6.946221995 + -0.5
N = -6.946221995 + -0.5

Combine like terms: -6.946221995 + -0.5 = -7.446221995
N = -7.446221995

Simplifying
N = -7.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {6.446221995, -7.446221995}

See similar equations:

| f(4)=-2x-5 | | 2/3x21-10 | | 8-9+0+3y-9= | | -3.6l=-71+35 | | 4b-5=15-b | | 3x+117= | | 7(p+2)=98 | | 6n^2-42n+72=0 | | 30=5(z-87) | | Ln(2x-7)=8 | | 2y-11=-12y-9 | | 5(f+2)=80 | | 13+7f=69 | | f(x)=6+x^2 | | 82=j-2 | | 147=21n | | 8=9+7xr | | x*0.0291=x*0.029+0.30 | | -14q=4a-126 | | N-5/2=-13 | | 9-5/(8-3)*2/6 | | x*0.03=x*0.029+0.30 | | x*0.032=x*0.029+0.30 | | x*0.035=x*0.029+0.30 | | -3.2m+7.6=-1.3 | | x*0.05=x*0.029+0.30 | | 13y+26=7y+22 | | 18x+60=1140 | | 10x-45=7-3x | | 2.984+2.926= | | 7p^2-77p+174=6 | | 1=2k/5(k-3) |

Equations solver categories