Solving a quadratic equation using the quadratic formula

Solving quadratic equations by factorisation is by far the easiest method. Sometimes, however, the quadratic equation will not factorise, so we must solve it by other means. Probably the second easiest method of solving a quadratic is by using the quadratic formula. All you have to do is put the numbers into the formula, work it through, and the answer will drop out.

For a quadratic:  ax2 + bx + c = 0 , you can find the value of x by using the formula:

Notice that there is a +/- sign in the equation. This means ‘plus or minus.’ This is because the quadratic equation has two solutions. Quadratics have two solutions because for any positive value of x2 there are two possible values of x, a positive value and a negative value. This is because if you multiply two negative numbers together, you get a positive answer. 

Eg: 22 = 2 x 2 = 4   but (-2)2 = -2 x -2 = 4

And it really is that simple. You can also solve quadratic equations which don’t factorise by completing the square.

See also: Quadratic graphs