Factorise and solve x^2 - 8x + 15 = 0.

Whenever faced with a quadratic equation in the form of AX^2 + BX + C = 0, the first thing you do is factorise it, which will look something like this: (X )(X ) = 0.You can see from this that when you multiply this out again, X x X = X^2, so you've dealt with the AX^2 part. in this question, A=1, as there is no number before X^2, but if, for example, it was 2X^2, you would then have (2X )(X ) = 0, as 2X x X = 2X^2. So back to our original question, we now have (X )(X ) = 0. Now what we do is very interesting; we find two numbers that multiply to make C, and sum to make B. So, in this case, two numbers that times to make 15, but sum to make -8. Now, because there's a minus there, we know there will be negative numbers involved. - x - = +, so two negative numbers must be multiplying to make 15 here. Let's try -5 and -3. -5 x -3 = 15. -5 + (-)3 = -8. So our two mystery numbers are -5 and -3. Let's put them inide the brackets: (X - 5)(X - 3) = 0. Now to solve this, we can split this into (X -5) = 0 and (X - 3) = 0. X - 5 = 0. X = 5. X -3 = 0. X = 3. So the equation has two possible solutions: X = 5, or X = 3.