Ryann Hart

2023-03-15

How to solve the equation for ${x}^{2}-3x=0$?

Sterling Cameron

${x}^{2}-3x=0$
$x\cdot \left(x-3\right)=0$ ($x$ was a common factor to both the terms)
In general, if $a\cdot b=0,$ then either $a=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}b=0$
So here,
$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x-3=0$
$x=0\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}}x=3$ is the correct Solution.
$Note$ :
Here's a classic $Mistake$ that many students make:Transpose $3x$ to the right hand side
${x}^{2}=3x$
Divide both sides by $x$ will give us $x=3$ (Incorrect/Incomplete)
This is a $mistake$ because we CANNOT divide by $x$ unless we are sure about it not being equal to zero.

Anastasia Macdonald

We must first factorize the equation in order to determine $x$.
${x}^{2}-3x=0$
As $x$ is the common factor between the 2 values, we factorize the equation by taking $x$ out of ${x}^{2}-3x=0$
${x}^{2}-3x=0$
$x\left(x-3\right)=0$
Any value that is multiplied by 0, will give 0 as the answer.
$1×0=0\phantom{\rule{0ex}{0ex}}2×0=0\phantom{\rule{0ex}{0ex}}3×0=0$
From here, we know that in $x\left(x-3\right)=0$,
$x=0$ and $\left(x-3\right)=0$
$\left(x-3\right)=0$
$x=3$
Hence $x=0$ and $x=3$

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