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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.

Method

We will take **[x**^{2} **+ 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}

Expand...

- Then expand the brackets,

(x + 4)^{2}

and you should get.....

x^{2} + 8x + 16

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

Take away and add...

- 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

Find the value of x...

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

(x + 4)^{2} – 9 = 0 :

You finish reading the completing in square in I/GCSE Mathematics.

Well done!