Question

How do you solve `x^2 - 20x = 0` by factoring?

Answer 1

The solutions are `x=0` and `20`.

Explanation:

First, split up `x^2` into `x*x` and `20x` into `x*20`.

Then, use the distributive property backward.

Lastly, set each of the factors equal to `0` and solve for `x` in each one:

`x^2-20x=0`

`color(red)x*color(blue)x-color(red)x*color(blue)20=0`

`(color(red)x)(color(blue)xcolor(blue)-color(blue)20)=0`

Setting each of the factors equal to `0`:

`color(white){color(black)( (color(red)x=0, qquadqquadcolor(blue)(x-20)=0), (color(red)x=0, qquadqquadcolor(blue)(x-20)color(green)+color(green)20=0color(green)+color(green)20), (color(red)x=0, qquadqquadcolor(blue)(x)color(red)cancel(color(blue)(-)color(blue)(20)color(green)+color(green)20)=0color(green)+color(green)20), (color(red)x=0, qquadqquadcolor(blue)(x)=0+20), (color(red)x=0, qquadqquadcolor(blue)x=20):}`

These are the solutions. Hope this helped!