How can I factorise a quadratic equation?

A quadratic equation is an equation of the form y = ax² + bx + c where a, b and c are constants (for example 5, -2 or 0). To "solve" a quadratic equation we are finding the values of x that satisfy this equation For example the equation 9 = x² has 2 solutions, x = 3 and x = -3 (as when you replace x with these values, the equation is true, as 9 = 9). A quadratic equation can either have 0, 1 or 2 solutions.

There are many ways of finding what values satisfy these equations, here is one that always works.

The quadratic formula: First rearrange your equation so that it is in the form 0 = ax² + bx + c now take the general quadratic formula which is given by x = (-b +- sqrt(b² - 4ac)) / 2a +- in this case means one solution is given by adding, and one by subtracting (so you have to do it twice). Simply substituting our coefficients into this formula will give us our solutions.

For example let's take the equation 7 = x² - 2x + 8

1) Rearrange to the appropriate format by moving the 7 onto the other side to give: x² -2x + 1 = 0

2) Work out our coefficients, a = 1 b = -2 c = 1

3) Substitute these into our equation to give:

x = -((-2) +- sqrt ( (-2)^2 - 411)) / 2

 This simplifies to give

x = (2 +- sqrt (4 - 4)) / 2

which simplfies again to 1 +- 0, this means we have only one solution (as 1 + 0 and 1 - 0 both = 1), so our solution to this is x = 1.