Question

X^2-2x=0
solve by completing the square

Answer 1

First, halve the second coefficient (-2) and then square it:
-2/2 = -1, (-1)^2 = 1, then add it to both sides:

`x^(2) -2x +1 = 1`
Now on the left side, we can rewrite this as:

`x^(2) - x - x + 1 = 1`
Factor out an x from the first two terms:

`x(x-1) - x + 1 = 1`
Factor out a -1 from the last two terms:

`x(x-1) - 1(x-1) = 1`
Now we can rewrite it as:

`(x-1)(x-1) = 1`
Which is equal to:

`(x-1)^(2) = 1`
Square root both sides, keeping in mind that leaves us with plus or minus one on the right:

`(x-1) = 1`

`(x-1) = -1`
Add one to both sides in both equations to solve for our two roots:

`x = 2, 0`

Answer 2

x^2 -2x = 0
Get the coefficient of x
divide it by 2
square it
add it to both sides
-2 / 2 = -1
-1^2 = 1
x^2 -2x +1= 1
Take the square root of both sides
(x-1) = sq root (1)