How do you solve #x^2=21x# graphically and algebraically?

1 Answer
Apr 10, 2016

Answer:

#x=0#
or
#x=21#
(see below for methods)

Explanation:

**Method 1: (Not recommended)
Graphically you could plot points for each of the equations
#color(white)("XXX")y_1=x^2#
and
#color(white)("XXX")y_2=21x#
on the same plane.

With a large enough sheet of paper you would find that the lines for the two equations intersect at #(0,0)# and at #(21,441)#
given the solutions for #x# as #0# or #21#

**Method 2: Algebraically
#color(white)("XXX")x^2=21x#
#color(white)("XXX")rarr x^2-21x=0#
#color(white)("XXX")rarr x(x-21)=0#
which is true if #(x=0)# or #(x=21)#