2n^2=16+9n

Simple and best practice solution for 2n^2=16+9n 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=16+9n equation:


Simplifying
2n2 = 16 + 9n

Solving
2n2 = 16 + 9n

Solving for variable 'n'.

Reorder the terms:
-16 + -9n + 2n2 = 16 + 9n + -16 + -9n

Reorder the terms:
-16 + -9n + 2n2 = 16 + -16 + 9n + -9n

Combine like terms: 16 + -16 = 0
-16 + -9n + 2n2 = 0 + 9n + -9n
-16 + -9n + 2n2 = 9n + -9n

Combine like terms: 9n + -9n = 0
-16 + -9n + 2n2 = 0

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

Divide each side by '2'.
-8 + -4.5n + n2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4.5n + 8 + n2 = 0 + 8

Reorder the terms:
-8 + 8 + -4.5n + n2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4.5n + n2 = 0 + 8
-4.5n + n2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4.5n + n2 = 8

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 = 8 + 5.0625

Reorder the terms:
5.0625 + -4.5n + n2 = 8 + 5.0625

Combine like terms: 8 + 5.0625 = 13.0625
5.0625 + -4.5n + n2 = 13.0625

Factor a perfect square on the left side:
(n + -2.25)(n + -2.25) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(n + -2.25) equal to 3.614208074 and -3.614208074.

Subproblem 1

n + -2.25 = 3.614208074 Simplifying n + -2.25 = 3.614208074 Reorder the terms: -2.25 + n = 3.614208074 Solving -2.25 + n = 3.614208074 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 = 3.614208074 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = 3.614208074 + 2.25 n = 3.614208074 + 2.25 Combine like terms: 3.614208074 + 2.25 = 5.864208074 n = 5.864208074 Simplifying n = 5.864208074

Subproblem 2

n + -2.25 = -3.614208074 Simplifying n + -2.25 = -3.614208074 Reorder the terms: -2.25 + n = -3.614208074 Solving -2.25 + n = -3.614208074 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 = -3.614208074 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + n = -3.614208074 + 2.25 n = -3.614208074 + 2.25 Combine like terms: -3.614208074 + 2.25 = -1.364208074 n = -1.364208074 Simplifying n = -1.364208074

Solution

The solution to the problem is based on the solutions from the subproblems. n = {5.864208074, -1.364208074}

See similar equations:

| x-90=45 | | 7x+3=-3x-71 | | 2x-3=7x+7 | | 3s-12s=36 | | 14v+-18v=16 | | 7x-3x+9=8x+5 | | 13-2y=9 | | 8x-2-5x+7=6x+8 | | 8n(4n+7)=17 | | (4x+3)(x+3)=184 | | 40.74=8g+3.86 | | -0.5(x+10)(x-6)=0 | | x=241.75+-0.25y | | 40.74=8g+386 | | P(x)=6x^5-47x^4+105x^3+9x^2-270x+216 | | h=18-17h | | 8z+19z=162 | | x+19+x-11+2x=180 | | -12+r=r+2r | | 8x=5y-15 | | (-1-I)^2/2 | | 4(-2x+10)=3x+6 | | -7+6n=-n+8n | | 4r-750r-2=0 | | (3x^2+2x+1)+(3x-8)-(x^2+6x-5)= | | 3x^2+13x+11=0 | | x(x+2)+5(x+2)=0 | | x/5=3/126 | | 3[6-f]-4=3f-4 | | 60=8+4p | | 8x-2-5x+7=6x+9 | | 8x-2-5x+7=6x+3 |

Equations solver categories