(17x-3)^2-2(17x-3)-15=0

Question

determine the appropriate substitution using the new variable u:u=

Answer 1

Hi Mel.

The appropriate substitution would be (17x-3),

this way you can rewrite the equation as a simple

quadratic equation:

 

u²-2u-15=0

 

Now you can factor this into

 

(u-5)(u+3)=0

 

Setting each factor =0, get

 

u-5=0  so u=5

 

and u+3 = 0 so u=-3

 

 

Now that we have u=5   or  u=-3,

 

substitute 17x-3 back in for each of the u's:

 

u=17x-3=5    or    u=17x-3 = -3

 

Add 3 to both sides         

 

17x=8         or        17x = 0

 

 

so x=8/17    or   x=0