SOLUTION: solve to find x. 16(x-1/x-8)^2+8(x-1/x-8)+1=0 u=(x-1)/(x-8) 16u^2+8u+1=0 (4u+1)(4u+1) 4u+1=0 u=1/4 (x-1/x-8)=1/4 what is the next step?

Question 295420: solve to find x.
16(x-1/x-8)^2+8(x-1/x-8)+1=0
u=(x-1)/(x-8)
16u^2+8u+1=0
(4u+1)(4u+1)
4u+1=0
u=1/4
(x-1/x-8)=1/4
what is the next step?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Your continuation:
4u+1=0
4u=-1
u=-1/4 not 1/4
u=(x-1)/(x-8)
-1/4=(x-1)/(x-8)
-1*(x-8)=4*(x-1)
-x*8=4x-4
12=5x
12/5=x
or from the beginning
16((x-1)/(x-8))^2+8*((x-1)/(x-8))+1=0
multiply the second term by (x-8)/(x-8)
and 1 by (x-8)^2)/(x-8)^2)
16((x-1)/(x-8))^2+8*((x-1)(x-8)/(x-8)^2)+(x-8)^2)/(x-8)^2)=0
which reduces to
(5x-12)^2/(x-8)^2 = 0
and then to
(5 x-12)^2 = 0
then
5x-12 = 0
then 5x=12
x=12/5

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