Question

Consider the equation:

x ^2 −4x+4=2x
1) Rewrite the equation by completing the square.
Your equation should look like (x+a)^2=b or (x-c)^2 =d

Answer 1

lusing completing square metjod

x

Explanation:

x^2_6x+(_3)^2=_4+9

(x_3)^2=5

x_3=

`√(5)`

`x = 3 + or - √(5)`

Answer 2

(x-3)^2 = 5

x = 3 ±sqrt(5)

Explanation:

x ^2 −4x+4=2x

Subtract 2x from each side

x ^2 −4x-2x+4=2x-2x

x^2 -6x +4 = 0

Subtract 4 from each side

x^2 -6x+4-4 =0-4

x^2 -6x = -4

Take -6

Divide by 2

-6/2 = -3

Square it

(-3)^2 = 9

Add to each side

x^2 -6x+9 = -4+9

(x-3)^2 = 5

Take the square root

sqrt((x-3)^2) = ±sqrt(5)

x-3 = ±sqrt(5)

Add 3 to each side

x = 3 ±sqrt(5)