Solving quadratic equations
Three methods: factorising, formula, completing the square. Pick the right one for the question.
Always rearrange to ax² + bx + c = 0 first. Try factorising; if not nice, formula. Higher: also completing the square (often when min/max is asked).
Worked examples
x² + 7x + 12 = 0 ⇒ (x+3)(x+4)=0 ⇒ x = −3 or −4.
x² + 5x + 1 = 0: formula gives x = (−5 ± √21)/2.
(x − 4)² = 9 ⇒ x − 4 = ±3 ⇒ x = 7 or 1.
Frequently asked questions
Why two solutions?
Quadratic curves cross the x-axis at up to 2 points. The two solutions are those crossing points.
How is ‘no real solutions’ possible?
The curve doesn't cross the x-axis. Discriminant negative confirms it.