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Solve X^2 +13X+48=12

It is first important to get the equation to equal 0, so to do this you minus 12 from each side of the equals symbol, giving you

X^2 +13X+36=0

Now it is time to think about factorising!

The best trick for this is to find two numbers that multiply together to make the number without any X's (36 in this case) AND add together to make the number with an X after it (13 in this case).

So start by listing the factors of 36 in pairs:

6,6

3.12

1.36

4,9

2,18

Then turn each into an addition

6+6=12

3+12=15

1+36=37

4+9=13

2+18=20

As 4+9 equal 13 we know that the two numbers in our brackets are 4 and 9! If we had not been able to make our number with addition, you could try with negative numbers (eg if our middle number was -5 we could make this by doing 4+-9=-5). Practice and knowing your times tables well will help you spot these easier.

So we factorise the equation into brackets

(X+4)(X+9) 

each bracket has to equal 0 so

X+4=0       X=-4

X+9=0        X=-9

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