9n^2-6n=17

Simple and best practice solution for 9n^2-6n=17 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^2-6n=17 equation:


Simplifying
9n2 + -6n = 17

Reorder the terms:
-6n + 9n2 = 17

Solving
-6n + 9n2 = 17

Solving for variable 'n'.

Reorder the terms:
-17 + -6n + 9n2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -6n + 9n2 = 0

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

Divide each side by '9'.
-1.888888889 + -0.6666666667n + n2 = 0

Move the constant term to the right:

Add '1.888888889' to each side of the equation.
-1.888888889 + -0.6666666667n + 1.888888889 + n2 = 0 + 1.888888889

Reorder the terms:
-1.888888889 + 1.888888889 + -0.6666666667n + n2 = 0 + 1.888888889

Combine like terms: -1.888888889 + 1.888888889 = 0.000000000
0.000000000 + -0.6666666667n + n2 = 0 + 1.888888889
-0.6666666667n + n2 = 0 + 1.888888889

Combine like terms: 0 + 1.888888889 = 1.888888889
-0.6666666667n + n2 = 1.888888889

The n term is -0.6666666667n.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667n + 0.1111111112 + n2 = 1.888888889 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667n + n2 = 1.888888889 + 0.1111111112

Combine like terms: 1.888888889 + 0.1111111112 = 2.0000000002
0.1111111112 + -0.6666666667n + n2 = 2.0000000002

Factor a perfect square on the left side:
(n + -0.3333333334)(n + -0.3333333334) = 2.0000000002

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(n + -0.3333333334) equal to 1.414213562 and -1.414213562.

Subproblem 1

n + -0.3333333334 = 1.414213562 Simplifying n + -0.3333333334 = 1.414213562 Reorder the terms: -0.3333333334 + n = 1.414213562 Solving -0.3333333334 + n = 1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + n = 1.414213562 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + n = 1.414213562 + 0.3333333334 n = 1.414213562 + 0.3333333334 Combine like terms: 1.414213562 + 0.3333333334 = 1.7475468954 n = 1.7475468954 Simplifying n = 1.7475468954

Subproblem 2

n + -0.3333333334 = -1.414213562 Simplifying n + -0.3333333334 = -1.414213562 Reorder the terms: -0.3333333334 + n = -1.414213562 Solving -0.3333333334 + n = -1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + n = -1.414213562 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + n = -1.414213562 + 0.3333333334 n = -1.414213562 + 0.3333333334 Combine like terms: -1.414213562 + 0.3333333334 = -1.0808802286 n = -1.0808802286 Simplifying n = -1.0808802286

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.7475468954, -1.0808802286}

See similar equations:

| 3.0=0.5(i) | | 5y+14=54 | | 2k-4.31=2.4k-4.99 | | -[x+3]+0.75x+5=0 | | (x*2+y*2)dx+(y*2-xy)dy=0 | | 3×m÷2/3=7 | | -5=2(s+19)-11 | | -20=9/-5 | | -1/2=-5/18(h) | | 3u-76-u=180 | | 6x^2-8=-105 | | -4b+3b+-4=13 | | 6=-2y+2x | | -19+6h=8h+19 | | 6s-17=s+43 | | 21=-x-3 | | 17d+20=-20+15d | | 2v-70=v | | 14=2(q-12) | | 6c-3=3c | | x-7=5x-11 | | 138x=5/8x^2 | | 12y+8x=268 | | -(j+-15)+-10=-1 | | 36/x-8=-2 | | 6.25x=7.25 | | 23-2m=3-15m-6 | | x+3+x+3=-(x+4+3x) | | -4b=-5b+13 | | 5x^3+10x^2-20x-40=0 | | 4=F-3 | | 4u-13=-u+17 |

Equations solver categories