What values of x make the equation x2 + 9x – 22 = 0 true? Check all that apply. –11 –2 0 2 11
Accepted Solution
A:
Answer: 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 ; ___________________________________ Answer: x = 2 ; -11 . ___________________________________