Tanvi solves x² = 7x like this: "Divide both sides by x, so x = 7." Explain her mistake, and find…

Step 1. The mistake. Dividing by $x$ is allowed only when $x \neq 0$. By dividing, she assumed that $x$ is not $0$, and so she threw away that case.

Step 2. The right way. $x^2 - 7x = 0$, so $x(x - 7) = 0$.

Step 3. Both roots. $x = 0$ or $x = 7$. Check: $0^2 = 7 \times 0$.