#47
Top 50 Mistake
Dividing by x and losing a solution
"The Vanishing Root"
The Mistake in Action
Solve $x^2 = 5x$
Wrong: Divide both sides by $x$: $x = 5$
Why It Happens
Students divide both sides by $x$, not realising that $x = 0$ is also a valid solution. Dividing by a variable can "lose" solutions.
The Fix
Never divide by the variable — it might be zero!
Instead, rearrange and factorise: $$x^2 = 5x$$ $$x^2 - 5x = 0$$ $$x(x - 5) = 0$$ $$x = 0 \text{ or } x = 5$$
You had two solutions, but dividing by $x$ lost the $x = 0$ case.
Spot the Mistake
Can you identify where this student went wrong?
Solve $x^2 = 5x$
Divide both sides by $x$: $x = 5$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: