Question

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

Answer 1

`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)`