Can you solve this problem 9xsquared-9x+2=0 x=

Question

9 x ² - 9x + 2 = 0

 

x=

Answer 1

9x^2-9x+2=0

9=3*3 and 2=1*2

use one 3 with 2 and the other 3 with 1

3*2==6 and3*1=3

6+3=9

(3x-2)(3x-1)=0

3x-2=0, 3x=2, x=2/3

3x-1=0, 3x=1, x=1/3

Answer 2

Have to choose 2 numbers in which their product is 18, and their sum is -9, therefore both have to be negative numbers.

 

     ab = 18     a+b = -9

 

     18 = 2 *9 = 6* 3 , so -6-3 = 18  , -6-3 =-9

 

     Split -9X to -6x- 3X

 

        9 X² - -9x +2 =0

 

         9 X² - 6X - 3X + 2 = 0

    

         3X ( 3X - 2 ) - ( 3X -2 ) = 0     factor by grouping

 

          ( 3 X - 2 ) ( 3X -1 ) =0

 

           3X - 2 = 0   X = 2/ 3       3X -1 = 0     X = 1/3

 

  This is a general rule:

 

 aX² + bX + c = 0

 

 choose 2 numbers m,n in such away

 

  that  ac = mn      and b/a = m+n

 where you have the values of a,b,c given in a quadratic equation.

 

 If m.n are integer values, then you can factor like the above example, otherwise use quadratic formula: 

Answer 3

See answer above by Parviz F.

Answer 4

Since 9*2=(-3)(-6), and -3-6 = -9,the coefficient of x, you can split -9x into -6x and -3x, and regroup

9x^2 - 9x + 2

= (9x^2 -6x) - (3x-2)

= 3x(3x-2) - (3x-2)

= (3x-2)(3x-1)

 

Solve (3x-2)(3x-1) = 0, x = 2/3, and x = 1/3