How do you solve the equation for x^2 - 3x = 0x23x=0?

2 Answers
Apr 8, 2015

x^2 - 3x = 0x23x=0

x*(x-3) = 0 x(x3)=0 (xx was a common factor to both the terms)

In general, if a*b = 0,ab=0, then either a = 0 or b = 0a=0orb=0

So here,
x = 0 or x - 3 = 0x=0orx3=0
color(green)( x = 0 or x = 3x=0orx=3 is the correct Solution.

color(red)(NoteNote :

Here's a classic color(red)(MistakeMistake that many students make:

Transpose 3x3x to the right hand side

x^2 = 3x x2=3x

Divide both sides by xx will give us x = 3x=3 (Incorrect/Incomplete)

This is a color(red)(mistakemistake because we CANNOT divide by xx unless we are sure about it not being equal to zero.

Apr 8, 2015

To find xx, we first have to factorize the equation.
x^2-3x=0x23x=0
As xx is the common factor between the 2 values, we factorize the equation by taking xx out of x^2-3x=0x23x=0

x^2-3x=0x23x=0
x(x-3)=0x(x3)=0

Any value that is multiplied by 0, will give 0 as the answer.
1x0=0
2x0=0
3x0=0

From here, we know that in x(x-3)=0x(x3)=0,
x=0x=0 and (x-3)=0(x3)=0

(x-3)=0(x3)=0
x=3x=3

Therefore x=0x=0 and x=3x=3