Question

Write x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers. (1 point)

(x − 4)2 = 3

(x − 3)2 = 2

(x − 2)2 = 1

(x − 1)2 = 4

Answer 1

x² - 6x + 7 = 0
x² - 6x = -7
x² - 6x + 9 = -7 + 9
(x-3)² = 2

Answer 2

B.
`(x-3)^2=2`.

Explanation:

We have been given an equation
`x^2-6x+7=0`. We are asked to write our given expression in form
`(x-a)^2=b`.

First of all, we will subtract 7 from both sides of our given equation.

`x^2-6x+7-7=0-7`

`x^2-6x=-7`

Now, we will complete the square for left side of equation by adding the half the square of 6.

`((6)/(2))^2=(3)^2=9`

Upon adding 9 on both sides of our equation, we will get:

`x^2-6x+9=-7+9`

`(x-3)^2=2`

Therefore, our required equation would be
`(x-3)^2=2` and option B is the correct choice.