Solve the quadratic equation by completing the square and by factoring.?

Question

x^2 - 20x = 0

x^2 - 20x + 100= 0+100... I think this is squaring the equation.

Can you show me how you got the - 10, please?

Answer 1

Yes, you started right for completing the square.
Continuing:

(x-10)^2 = 100

x-10 = +/-10

x= 10 +/- 10 = 20 or 0


To solve by factoring:

x(x-20) = 0

x=0 or x-20 = 0

x= 0 or x=20


Edited to add:
On the first step:
You factor x^2-20x+100 as a trinomial square by taking the square root of 100, and keeping the middle sign as is, so that's how we get (x-10)^2

As a teacher, I have to say great job on asking specific questions about the steps in the solution!

Answer 2

x^2 - 20x = 0
x^2 - 20x + 100= 0+100
(x-10)^2 = 100
x-10 = 10
x = 0

Answer 3

x^2-20x =0
it it is of the form (x-a)^2 = b
then x^2-2ax +a^2 = b
we have x^2-20x =0
2ax = 20x
a = 10
so add a^2 or 100 on both sides
(x-10)^2 = 10^2
x-10= +10/-20
but all above steps are not necessary as we can take x
x(x-20) = 0

Answer 4

Factoring: factor out the x:

x(x - 20) = 0
x = 0, 20

Answer 5

factored
x(x-20) = x^2-20x
x=0 , x =20

Answer 6

HOW CAN SOMETHING EQUAL NOTHING ?
THE PREMISE IS INCORRECT TO BEGIN WITH AND CANNOT BE SOLVED