Question

Write x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers.

A). (x − 4)2 = 3
B). (x − 3)2 = 2
C). (x − 2)2 = 1
D). (x − 1)2 = 4

Answer 1

the best answer is B

Answer 2

x² − 6x + 7 = 0

Let's complete the square [x²-6x+(??)²] -(??)² +7 = 0

As you noticed we have added the unknown square & also subtract the same so that not to change the equation

The question now is to calculate this square (??)²

We know that the middle term (6x) is twice the square root of the 1st times the square root of the 2nd, That is 6x=2x (multiply) √(??)²

6x = 2x?? & ??=6x/2x===> ?? =3 & (??)² =9

Hence plug (??)² into the equation above:

x² - 6x + 9 - 9 +7 =0

(x²-6x+9) -9 + 7 =0

(x-3)² -2 =0 ====> (x-3)² = 2 (that is B)