Using the quadratic formula

Using the technique of completing the square, you can make a formula which works for all quadratic equations.

• The most general way to write a quadratic equation is:
• ax² + bx + c = 0

• Here a, b and c are numbers that vary for different equations.
• So if the equation was:
• 2x² + 7x + 11 = 0
• then a = 2, b = 7, c = 11.

The formula for the solution is:

This formula will work for all equations that can be solved.

Always try to factorise first. If the equation factorises, this is the easier method. In an exam, any question that asks for an answer to a quadratic equation correct to x decimal places should be solved using this formula. Take a look at this example:

• Solve 2x² - 5x - 6 = 0
• Here a = 2, b = -5, c = -6

Substituting these values in the formula, gives you: