Question

Place the following steps in order to complete the square and solve the quadratic equation, x^2 - 6x + 7 = 0.

Answer 1

`x^2-6x=-7`

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

`(x-3)^2=2`

`√((x-3)^2)=\pm√(2)`

`(x-3)=\pm√(2)`

`x-3=3\pm√(2)`

Explanation:

The given quadratic equation is

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

Subtract 7 from both sides.

`x^2-6x=-7` ...(1)

If an expression is
`x^2+bx`, then we add
`((b)/(2))^2` to make it perfect square.

`((b)/(2))^2=((-6)/(2))^2=9`

Add 9 on both sides in equation (1).

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

`(x-3)^2=2`
`[\because (a-b)^2=a^2-2ab+b^2]`

Taking square root on both sides.

`√((x-3)^2)=\pm√(2)`

`(x-3)=\pm√(2)`

Add 3 on both sides.

`x-3=3\pm√(2)`

Therefore, the correct order is F, A, D, C, E and B.

Answer 2

option f

option a

option d

option c

option e

option b

Explanation:

we have x^2 - 6x + 7 = 0

f) x^2 - 6x = -7

a) x^2 - 6x + 9 = -7+9

d) (x-3)^2=2

c)
`\sqrt{(x-3)^(2)} = +-√(2)`

e) x-3=+-
`√(2)`

b) x=3+-
`√(2)`