9n^2=-10n+9

Simple and best practice solution for 9n^2=-10n+9 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 9n^2=-10n+9 equation:


Simplifying
9n2 = -10n + 9

Reorder the terms:
9n2 = 9 + -10n

Solving
9n2 = 9 + -10n

Solving for variable 'n'.

Reorder the terms:
-9 + 10n + 9n2 = 9 + -10n + -9 + 10n

Reorder the terms:
-9 + 10n + 9n2 = 9 + -9 + -10n + 10n

Combine like terms: 9 + -9 = 0
-9 + 10n + 9n2 = 0 + -10n + 10n
-9 + 10n + 9n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
-9 + 10n + 9n2 = 0

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

Divide each side by '9'.
-1 + 1.111111111n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.111111111n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.111111111n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.111111111n + n2 = 0 + 1
1.111111111n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.111111111n + n2 = 1

The n term is 1.111111111n.  Take half its coefficient (0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
1.111111111n + 0.3086419752 + n2 = 1 + 0.3086419752

Reorder the terms:
0.3086419752 + 1.111111111n + n2 = 1 + 0.3086419752

Combine like terms: 1 + 0.3086419752 = 1.3086419752
0.3086419752 + 1.111111111n + n2 = 1.3086419752

Factor a perfect square on the left side:
(n + 0.5555555555)(n + 0.5555555555) = 1.3086419752

Calculate the square root of the right side: 1.143958905

Break this problem into two subproblems by setting 
(n + 0.5555555555) equal to 1.143958905 and -1.143958905.

Subproblem 1

n + 0.5555555555 = 1.143958905 Simplifying n + 0.5555555555 = 1.143958905 Reorder the terms: 0.5555555555 + n = 1.143958905 Solving 0.5555555555 + n = 1.143958905 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = 1.143958905 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = 1.143958905 + -0.5555555555 n = 1.143958905 + -0.5555555555 Combine like terms: 1.143958905 + -0.5555555555 = 0.5884033495 n = 0.5884033495 Simplifying n = 0.5884033495

Subproblem 2

n + 0.5555555555 = -1.143958905 Simplifying n + 0.5555555555 = -1.143958905 Reorder the terms: 0.5555555555 + n = -1.143958905 Solving 0.5555555555 + n = -1.143958905 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5555555555' to each side of the equation. 0.5555555555 + -0.5555555555 + n = -1.143958905 + -0.5555555555 Combine like terms: 0.5555555555 + -0.5555555555 = 0.0000000000 0.0000000000 + n = -1.143958905 + -0.5555555555 n = -1.143958905 + -0.5555555555 Combine like terms: -1.143958905 + -0.5555555555 = -1.6995144605 n = -1.6995144605 Simplifying n = -1.6995144605

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.5884033495, -1.6995144605}

See similar equations:

| -u/4=24 | | p^2+10p+c=0 | | 3x(-4)-4x-5/1 | | 5x-3(2x-4)=2(x-1)+4 | | 7j=16j-18 | | 7=y+9 | | p^2-5p+c=0 | | 3n-8=n+15 | | z^2+18z+c=0 | | 144=36m^2 | | 5+4x-4=-23 | | 8x^2+16x+76=0 | | 10x+20=5x+40 | | 6(1+4m)=-9(6m-3) | | 3/(5-2x)=7/2 | | 0=16t^2+64t+512 | | (10x/2x-3)-5x/1 | | 3x+9+7y+3+15z-9=180 | | 10x-5/(2x-3) | | 13x-28=7x-4 | | k+8=k+2 | | -24+3[4y+2(5y-8)]-9y=0 | | Y=x^2+2x+60 | | y^2+5y+c=0 | | 20=u/3-15 | | 4x-25=9 | | 3x+6+2x-1+90= | | Y=33x+16 | | 3abx-7ba= | | 3-2x=4x-5 | | 23abx-5ba= | | 7x-8=x-44 |

Equations solver categories