n^2+3n+-6=0

Simple and best practice solution for n^2+3n+-6=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+3n+-6=0 equation:


Simplifying
n2 + 3n + -6 = 0

Reorder the terms:
-6 + 3n + n2 = 0

Solving
-6 + 3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + 3n + n2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
3n + n2 = 6

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 = 6 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 6 + 2.25

Combine like terms: 6 + 2.25 = 8.25
2.25 + 3n + n2 = 8.25

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(n + 1.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

n + 1.5 = 2.872281323 Simplifying n + 1.5 = 2.872281323 Reorder the terms: 1.5 + n = 2.872281323 Solving 1.5 + n = 2.872281323 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 = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 2.872281323 + -1.5 n = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 n = 1.372281323 Simplifying n = 1.372281323

Subproblem 2

n + 1.5 = -2.872281323 Simplifying n + 1.5 = -2.872281323 Reorder the terms: 1.5 + n = -2.872281323 Solving 1.5 + n = -2.872281323 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 = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -2.872281323 + -1.5 n = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 n = -4.372281323 Simplifying n = -4.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.372281323, -4.372281323}

See similar equations:

| 12.3=0.4-x | | 20x^3-4x^2-72x=0 | | x+9=9x^3+9x^2 | | 6x+36/8-x-2=0.25 | | -7q+62=-2q+12 | | 9x+7=4x+52 | | 14000=-2000+20000 | | 1/5(5x+8)=7 | | 12*1= | | b/(9+b*1)=1/13 | | h+1/3=4 | | 5N(2N-1)=0 | | b/(9+b*4)=1/13 | | 4a-66a*65744(-555)a=16 | | 2+x/4-5x-2/12=8-2x/5 | | x-0.25x+25=250 | | -4x-2-1(8x+1)=-1(-2x-10) | | 5.1x-1=4.1x | | 7x-9=24-4y | | 6x+7=6(x+9) | | 9-6x-3x-8=8+6x+4x-2+2 | | 2x+1/54x^2=0 | | 3-5y=6y-2 | | 5(x+2)=x+16 | | 1+2x+3x+4x=5x+6 | | X^2+54/x=0 | | 16/n=3/5 | | b+4/5=9/10 | | 5x/4-1/2=-3/16 | | 6-3x=1-2x | | g+4/5=219 | | 3/2x^1/2-3x^-1/2=0 |

Equations solver categories