I/GCSE Mathematics: Completing the square

This is a different method of solving quadratic formulas in I/GCSE Mathematics.

In I/GCSE Mathematics, it is called ‘Completing the Square’ because of the method where you:

1) write down a squared bracket, and then

2) put a number on the end to ‘Complete’ it.

We will take [x² + 8x + 7 = 0] as an example in the following.

• First check the quadratic equation* all equals to 0.

In this case it is.

• Then half the coefficient* of x.

8 ÷ 2 = 4

• This is the number that goes inside the squared bracket.

Thus (x + 4)²

• Then expand the brackets,

(x + 4)²

and you should get.....

x² + 8x + 16

• But we haven’t got a +16 in our quadratic equation so.....

• We then take away 16 and add 7 from the quadratic equation.

(x + 4)² – 16 +7 = 0

• When we simplify this we get:

(x + 4)² – 9 = 0

Finally we must find the value of x by rearranging the equation

(x + 4)² – 9 = 0 :

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