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Solve for x in the equation x2 - 2x - 35 = 0.

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3 Answers

Hi Angela,
 
x2-2x-35=0
x2-7x+5x-35=0
x(x-7)+5(x-7)=0
(x-7)(x+5)=0
x-7=0      or  x+5=0
x=7         or  x=-5
 
Check: x=7 ,LHS = 49-14-35
                          =0 =RHS
           x=-5, LHS = 25+10-35
                           =0=RHS
Ans: x=7 or x=-5
 
 
Meena from Strongsville,OH
This is a trinomial, and anytime the instructions call for factoring, first look for a GCF, but there is none in this problem. To factor a trinomial, use the AC method. AC means A*C, which is -35x2. You need to find two terms that multiply to get -35x2, but at the same time they need to add or subtract to get B, which is -2x. Make a T chart, and start listing the factors of -35, that add or subtract to get -2.
 
Because they have to mulitply to get a negative, and add or subtract to get a negative, then they must be different signs with the negative being larger. 5 and -7 will be the two factors to use. Now you can rewrite the problem as   (x+5) (x-7) =0 
 
To find out what x is, set each of the factors equal to 0, x+5=0  and x-7=0
On the first one, subtract 5 from both sides, and you get.....
On the second one, add 7 to both sides, and you get........
 
 
 
 
Hi Angela
 
To solve this quadratic equation, we need to factor.  We can brake the x2-2x-35=0 into two factors:
x2-2x-35=0
(x-7)(x+5)=0
 
Then we set each factor equal to zero and solve for x:
(x-7)=0                  (x+5)=0
  x=7                        x=-5
 
So the answer is x=7 and x=-5