n^2+19n+66=0

Simple and best practice solution for n^2+19n+66=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+19n+66=0 equation: 


Simplifying
n2 + 19n + 66 = 0

Reorder the terms:
66 + 19n + n2 = 0

Solving
66 + 19n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '-66' to each side of the equation.
66 + 19n + -66 + n2 = 0 + -66

Reorder the terms:
66 + -66 + 19n + n2 = 0 + -66

Combine like terms: 66 + -66 = 0
0 + 19n + n2 = 0 + -66
19n + n2 = 0 + -66

Combine like terms: 0 + -66 = -66
19n + n2 = -66

The n term is 19n.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19n + 90.25 + n2 = -66 + 90.25

Reorder the terms:
90.25 + 19n + n2 = -66 + 90.25

Combine like terms: -66 + 90.25 = 24.25
90.25 + 19n + n2 = 24.25

Factor a perfect square on the left side:
(n + 9.5)(n + 9.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(n + 9.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
n + 9.5 = 4.924428901

Simplifying
n + 9.5 = 4.924428901

Reorder the terms:
9.5 + n = 4.924428901

Solving
9.5 + n = 4.924428901

Solving for variable 'n'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + n = 4.924428901 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + n = 4.924428901 + -9.5
n = 4.924428901 + -9.5

Combine like terms: 4.924428901 + -9.5 = -4.575571099
n = -4.575571099

Simplifying
n = -4.575571099


Subproblem 2
n + 9.5 = -4.924428901

Simplifying
n + 9.5 = -4.924428901

Reorder the terms:
9.5 + n = -4.924428901

Solving
9.5 + n = -4.924428901

Solving for variable 'n'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + n = -4.924428901 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + n = -4.924428901 + -9.5
n = -4.924428901 + -9.5

Combine like terms: -4.924428901 + -9.5 = -14.424428901
n = -14.424428901

Simplifying
n = -14.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-4.575571099, -14.424428901}

See similar equations:

| -3+24=m-6 | | -2n+5m-8=0 | | x=14-2 | | 122=10x-48 | | (X+1)(x+1)=x(x-7)+19 | | 8d-4d-6d-8=2d+8 | | 32x+4-18x-10=22 | | 4x+12=4x+5 | | (y+85)+y+(y-50)=425 | | x+3+45=18 | | 0.96-8.5= | | 3(q-5)=2(+5) | | x+3+45=188 | | 4z^2+11z+4=7 | | (a+b)-ab= | | 62h+5-1.4h=4.8h+5 | | 10m=2(m+2) | | h(t)=16t^2+2421 | | 10x(x-3)=0 | | -.231x^2+x+-2.16=0 | | -8x+9+2x+-4=-5 | | 9+y=1.5x | | 5-5(p+2)-3p=-5-8p | | 2y+27=-5y | | 3s^2+s-24= | | 3(-11-5m)=7(1-5m) | | 12w+19w-4+1=-2w+1-4 | | 10+6z=19+4z | | 8-3x=20-9x | | (x+90)+x+(x-17)=388 | | A=(32)-(9)(2) | | 8(1+5x)+5=13+5xC |

Equations solver categories