Mixed Practice: Linear & Quadratic

In an exam nobody whispers "this one is quadratic". Classification is step zero:

1. Simplify/expand if needed. What is the highest power of $x$?
2. Power 1 → linear toolkit: gather, isolate, divide.
3. Power 2 → rearrange to $= 0$, then factor / roots / formula.

Classification traps:

• $x(x - 3) = 10$ looks factored but hides $x^2 - 3x - 10 = 0$ — quadratic.
• $x^2 + 2x = x^2 - 6$ looks quadratic, but the $x^2$'s cancel: $2x = -6$ — linear!

Misclassify and you waste minutes or lose roots. Classify first, then execute the routine you have drilled.