Question

If 3x^2-2x+7=0, then (x-1/3)^2=

A 20/9
B 7/9
C -7/9
D -8/9
E -20/9

Answer 1

one approach
expand (x-1/3)^2 and substitute 3x^2 -2x+ 7 = 0 then simplify

Answer 2

Ok so should i substitute (x-1/3)^2 into the other one?

Answer 3

is this what the first one looks like expanded?

x^2-2/3+1/9

Answer 4

another approach
to factor complete the square
3x^2 -2x + 7 = 0
divide by 3
(x-b/a)^2 = (x-2/6)^2 = (x-1/3)^2 you had to add 1/9

Answer 5

*should be b/2a

Answer 6

To factor that equation you said i should divide by three first?

Answer 7

you will get the same result
3x^2-2x + 7 = 0
x^2 -2/3 + 7/3 =0
(x-2/6)^2 + 1/9 + 7/3 = 0
(x-1/3)^2 = 0-1/9-7/3 =
do you see E

Answer 8

Ohh yes i see that thank you so much you're awesome :)

Answer 9

wait i think i have a calculation error

Answer 10

i have a question did u substitute the other equation or where did u get 2/6?

Answer 11

(x-2/6)^2 + 1/9 + 7/3 = 0
I added 1/9 to the left so i need 1/9 on the right

Answer 12

Oh thats right

Answer 13

Alright i'll do this once again and see if i can get the same answer :)

Answer 14

it's ok I actually did it but i did not write it on the entry posted
1/9 -7/3 = 1/9-21/9 = -20/9 answer E

Answer 15

when you complete the square x-b/2a
a = 3 b = 2
2*a = 2*3 = 6

Answer 16

(a +b)^2 = a^2 + 2ab + b^2 you have 2ab when expanded

Answer 17

thanks a lot you're a great help :)