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

1 Answer
Mar 10, 2018

Answer:

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!