2n^2+9n+11=3

Simple and best practice solution for 2n^2+9n+11=3 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 2n^2+9n+11=3 equation:


Simplifying
2n2 + 9n + 11 = 3

Reorder the terms:
11 + 9n + 2n2 = 3

Solving
11 + 9n + 2n2 = 3

Solving for variable 'n'.

Reorder the terms:
11 + -3 + 9n + 2n2 = 3 + -3

Combine like terms: 11 + -3 = 8
8 + 9n + 2n2 = 3 + -3

Combine like terms: 3 + -3 = 0
8 + 9n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
4 + 4.5n + n2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 4.5n + -4 + n2 = 0 + -4

Reorder the terms:
4 + -4 + 4.5n + n2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 4.5n + n2 = 0 + -4
4.5n + n2 = 0 + -4

Combine like terms: 0 + -4 = -4
4.5n + n2 = -4

The n term is 4.5n.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5n + 5.0625 + n2 = -4 + 5.0625

Reorder the terms:
5.0625 + 4.5n + n2 = -4 + 5.0625

Combine like terms: -4 + 5.0625 = 1.0625
5.0625 + 4.5n + n2 = 1.0625

Factor a perfect square on the left side:
(n + 2.25)(n + 2.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(n + 2.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

n + 2.25 = 1.030776406 Simplifying n + 2.25 = 1.030776406 Reorder the terms: 2.25 + n = 1.030776406 Solving 2.25 + n = 1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + n = 1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + n = 1.030776406 + -2.25 n = 1.030776406 + -2.25 Combine like terms: 1.030776406 + -2.25 = -1.219223594 n = -1.219223594 Simplifying n = -1.219223594

Subproblem 2

n + 2.25 = -1.030776406 Simplifying n + 2.25 = -1.030776406 Reorder the terms: 2.25 + n = -1.030776406 Solving 2.25 + n = -1.030776406 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + n = -1.030776406 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + n = -1.030776406 + -2.25 n = -1.030776406 + -2.25 Combine like terms: -1.030776406 + -2.25 = -3.280776406 n = -3.280776406 Simplifying n = -3.280776406

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-1.219223594, -3.280776406}

See similar equations:

| -4x^2-4x+4=5 | | 5y=4x-7 | | (2x-8)(7x-5)=0 | | 2x^2+4x-1=-3 | | -4n^2+3n-5=5 | | 18x+7=151 | | 9q-6q+3=12 | | (2r-130)-(6r+4)= | | 8r^2=19-12r | | ax^2+10x+16=0 | | x=.8(180-x) | | 9m^2+10m=5 | | 50-3x=65 | | 3x+2+12x-17=90 | | 135=xy | | 9n^2=7 | | -(5y+3)-(4y-6)=-3 | | -12x=-20y-20 | | 2x^2-x^2-16x+12=0 | | 6x+2+2x=34 | | 3y/315/3 | | 999999999+9999999= | | 6cups= | | -3(3s-5)-15=-2(8s+5)-2 | | x(x+4)=130 | | K(3)=133-2 | | 16-7d=4h-30 | | 12x^2-10x=x^2+4x | | 6-2/x=10 | | 0.65x+0.05(6-x)=0.10(51) | | x+(x-28)=90 | | 0.16(12)+0.04x=0.08(6+x) |

Equations solver categories