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How would you solve a quadratic equation by factorising?

Solve the equation :  x2 - 8x + 15

The first step is to factorise the quadratic equation.

1. You must find two numbers which will add to give -8 and multiply to give 15. 

The numbers that would do this are -5 and -3. 

Therefore (x-5) (x-3). To check whether this is correct, you can expand the brackets and it should give you the equation you first started with. 

The second step is to find the value of x.

2. For this you must equate each bracket to 0. 

(x-5)= 0       and   (x-3)=0

Now solve : x = 5    and   x= 3

The third step is subsitution 

3. Finally to check this is correct. Substitute the values of x into the equation.

 x2 - 8x + 15

-Subsitute x =5

52-8 x 5 +15 = 0

25-40+15 = 0 

-Subsitute x=3

3- 8 x 3 +15 = 0

9-24+15=0 

These 3 simple steps will help you solve any quadratic equation. 

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