9n^2-2n=10

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


Simplifying
9n2 + -2n = 10

Reorder the terms:
-2n + 9n2 = 10

Solving
-2n + 9n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -2n + 9n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -2n + 9n2 = 0

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

Divide each side by '9'.
-1.111111111 + -0.2222222222n + n2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -0.2222222222n + 1.111111111 + n2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -0.2222222222n + n2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -0.2222222222n + n2 = 0 + 1.111111111
-0.2222222222n + n2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-0.2222222222n + n2 = 1.111111111

The n term is -0.2222222222n.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222n + 0.01234567901 + n2 = 1.111111111 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222n + n2 = 1.111111111 + 0.01234567901

Combine like terms: 1.111111111 + 0.01234567901 = 1.12345679001
0.01234567901 + -0.2222222222n + n2 = 1.12345679001

Factor a perfect square on the left side:
(n + -0.1111111111)(n + -0.1111111111) = 1.12345679001

Calculate the square root of the right side: 1.059932446

Break this problem into two subproblems by setting 
(n + -0.1111111111) equal to 1.059932446 and -1.059932446.

Subproblem 1

n + -0.1111111111 = 1.059932446 Simplifying n + -0.1111111111 = 1.059932446 Reorder the terms: -0.1111111111 + n = 1.059932446 Solving -0.1111111111 + n = 1.059932446 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = 1.059932446 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = 1.059932446 + 0.1111111111 n = 1.059932446 + 0.1111111111 Combine like terms: 1.059932446 + 0.1111111111 = 1.1710435571 n = 1.1710435571 Simplifying n = 1.1710435571

Subproblem 2

n + -0.1111111111 = -1.059932446 Simplifying n + -0.1111111111 = -1.059932446 Reorder the terms: -0.1111111111 + n = -1.059932446 Solving -0.1111111111 + n = -1.059932446 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + n = -1.059932446 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + n = -1.059932446 + 0.1111111111 n = -1.059932446 + 0.1111111111 Combine like terms: -1.059932446 + 0.1111111111 = -0.9488213349 n = -0.9488213349 Simplifying n = -0.9488213349

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.1710435571, -0.9488213349}

See similar equations:

| n.4/5=1 | | 4x-8=2x+28 | | 6y-16=3(4-p) | | 12-3(x-5)=2(x-4)+5 | | .5(m+9)=6 | | 8.5x=-85 | | 0.12x+8.2=4.2(3x-2.1) | | 8.5=85 | | 8.5=-85 | | 6-5x=4(1-x) | | 55g-132n= | | 1/x-1/4=-1/2 | | 3w^2=363 | | 6x+2=4x+28 | | 3x-8=x+62 | | (10+25)=5 | | 7(z+2)=6z | | w-9=26 | | .5x^2=512 | | f(x)=(x-8)-9 | | 2/x+4=6/x | | -4(8x+3)=17-3x | | (x+5)-logx=3 | | x/6+2/3=-5/3 | | x/5+x=6 | | 0.7+1.2=0.8x-2.4 | | 3z+9-z=10+z+9 | | f(x)=(x+6)-16 | | 16x=2,864 | | x/3+x/6=2 | | x^3+5x^2+x-75=0 | | 7.3t+22=2.1+-22.2 |

Equations solver categories