9x^2-6x-65=0

Simple and best practice solution for 9x^2-6x-65=0 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 9x^2-6x-65=0 equation: 


Simplifying
9x2 + -6x + -65 = 0

Reorder the terms:
-65 + -6x + 9x2 = 0

Solving
-65 + -6x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-7.222222222 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '7.222222222' to each side of the equation.
-7.222222222 + -0.6666666667x + 7.222222222 + x2 = 0 + 7.222222222

Reorder the terms:
-7.222222222 + 7.222222222 + -0.6666666667x + x2 = 0 + 7.222222222

Combine like terms: -7.222222222 + 7.222222222 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 7.222222222
-0.6666666667x + x2 = 0 + 7.222222222

Combine like terms: 0 + 7.222222222 = 7.222222222
-0.6666666667x + x2 = 7.222222222

The x term is -0.6666666667x.  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.
-0.6666666667x + 0.1111111112 + x2 = 7.222222222 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 7.222222222 + 0.1111111112

Combine like terms: 7.222222222 + 0.1111111112 = 7.3333333332
0.1111111112 + -0.6666666667x + x2 = 7.3333333332

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 7.3333333332

Calculate the square root of the right side: 2.708012802

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 2.708012802 and -2.708012802.


Subproblem 1
x + -0.3333333334 = 2.708012802

Simplifying
x + -0.3333333334 = 2.708012802

Reorder the terms:
-0.3333333334 + x = 2.708012802

Solving
-0.3333333334 + x = 2.708012802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 2.708012802 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 2.708012802 + 0.3333333334
x = 2.708012802 + 0.3333333334

Combine like terms: 2.708012802 + 0.3333333334 = 3.0413461354
x = 3.0413461354

Simplifying
x = 3.0413461354


Subproblem 2
x + -0.3333333334 = -2.708012802

Simplifying
x + -0.3333333334 = -2.708012802

Reorder the terms:
-0.3333333334 + x = -2.708012802

Solving
-0.3333333334 + x = -2.708012802

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -2.708012802 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -2.708012802 + 0.3333333334
x = -2.708012802 + 0.3333333334

Combine like terms: -2.708012802 + 0.3333333334 = -2.3746794686
x = -2.3746794686

Simplifying
x = -2.3746794686


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.0413461354, -2.3746794686}

See similar equations:

| 3x^2-9x+54=0 | | 5*a*a=40 | | n-18-4n= | | e^3x=52 | | n^2= | | 7.5x-2.8x=1.45 | | 5*a=40 | | 5x-10=90 | | 3y-2y=-5 | | x^2+16=25 | | 13-10x=77-24x | | y-(-7)= | | 6x+3y=32 | | 3x^2+2x^2+x=0 | | 15=18t-11t | | 4x^2-14x-60=0 | | -6(x+3)-13=12+5 | | m+7=4 | | 2z=18-34 | | x^3+2x^2+x=-1 | | 14c=6c-19 | | 5x^2=-375 | | 3g=-8+2g | | 77-3x=15x+19 | | 13=3x-8 | | 14-7x=116-28x | | 4w+3=13 | | 0.2x=5.6 | | 4=9+y | | 8x-(6x+8)=-2 | | 1.5-x=8.7 | | 4m+8n-7(7m-6n)= |

Equations solver categories