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

##### 1 Answer
Apr 10, 2016

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

#### Explanation:

**Method 1: (Not recommended)
Graphically you could plot points for each of the equations
$\textcolor{w h i t e}{\text{XXX}} {y}_{1} = {x}^{2}$
and
$\textcolor{w h i t e}{\text{XXX}} {y}_{2} = 21 x$
on the same plane.

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

**Method 2: Algebraically
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} = 21 x$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow {x}^{2} - 21 x = 0$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x \left(x - 21\right) = 0$
which is true if $\left(x = 0\right)$ or $\left(x = 21\right)$