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

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4 Answers

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
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
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 X- -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:
 
 aX+ 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: