Quadratic equations: watch it solved step by step

Factorise, complete the square or use the formula, then check each root. Level: GCSE / A-level. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: 2x^2 + 7x + 3 = 0

1. The equation. A quadratic equation has an x² term. It can have two solutions, one, or none. We will find them step by step, then check each one.
2. Find two numbers: product 6, sum 7. Multiply a × c = 2 × 3 = 6. We need two numbers that multiply to 6 and add to 7 (the middle coefficient). Trying factor pairs: the pair 1 and 6 works.
3. Split the middle term. Rewrite 7x as 1x + 6x (they add to the same thing).
4. Factorise in pairs. Take the common factor out of the first two terms and out of the last two. Both groups now contain the same bracket (2x + 1).
5. Factorise the bracket out. Since the bracket is common, factorise it out: (2x + 1)(x + 3).
6. Zero product rule. If two things multiply to give 0, at least one of them is 0. So set each bracket equal to 0.
7. Solve each bracket. Solve the two small equations.
8. The solution. There are two solutions.
9. Check each solution. Put each solution back into the equation: it must give 0.

Answer: x = -1/2 or x = -3

Practise quadratic equations with problems the Lab marks for you.