What values of x make the equation x2 + 9x – 22 = 0 true? check all that apply. –11 –2 0 2 11

  x = 2 ;  -11 .

Explanation:

Given the equation:

  x² + 9x − 22 = 0  ;  Solve for:  "x" ;


Let us factor the "left-hand side" of the equation:

  "x² + 9x − 22"  ;


What are the factors of "-22"" that add up to "positive 9" ?

  Let us list the factors of "-22" :

-2, 11;  → -2 + 11 = 9 ;
-11, 2;  → -11 + 2 = -9 ;


So we have:  "-2" and "11" ;

So;     "x² + 9x − 22" ; factors into " (x−2)(x + 11)" ;

We have:  (x−2)(x + 11) = 0 ;

So:  x − 2 = 0 ;  

Add "2" to each side of the equation; 

     x − 2 + 2 = 0 + 2 ; 

          x = 2 ; 

   x + 11 = 0 ;

Subtract "11" from each side of the equation;

   x + 11 − 11 = 0 − 11 ;

      x = -11 ; 

   x = 2 ; -11 .

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