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

Question

solve for x in the equation  x^2-2x-35=0

Answer 1

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

Answer 2

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........

 

 

 

 

Answer 3

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