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

2 Answers
Apr 8, 2015

x^2 - 3x = 0

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

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

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

color(red)(Note :

Here's a classic color(red)(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 color(red)(mistake because we CANNOT divide by x unless we are sure about it not being equal to zero.

Apr 8, 2015

To find x, we first have to factorize the equation.
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(x-3)=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)=0,
x=0 and (x-3)=0

(x-3)=0
x=3

Therefore x=0 and x=3