How do you solve #x(x-7)=0#?

1 Answer
Nov 1, 2015

Answer:

#x=0#
or
#x=7#

Explanation:

The format of this queston is already in factored form. This makes it quite easy to solve for #x#. They key to this is to know that anything multiplied by #0# is #0#. We have two things multiplied by each other:

#x# multiplied by #(x-7)# = #0#

So, this means, that if either term is equal to zero, the whole equation will equal to zero.

The first term is just #x#, so #x=0# is the first solution.

The second term is #(x-7)#. We need to set that equal to zero and solve for #x#.
#x-7=0#
#x=7# which is our second solution.

To check, plugging back into #x(x-7)=0#:

For #x=0#
#0(-7)=0#
#0=0#
so it works.

For #x=7#
#7(7-7)=7(0)=0#
#0=0#
which also works.