Using factorization, solve x^2 + 10x + 24 = 0

To factorize the equation we need to find two numbers a and b such that

a * b = 24 and

a + b = 10

By closely looking at those, we find that 4 and 6 satisfy both conditions, as

6 + 4 = 10 and

6 * 4 = 24

The next step is to split the middle term 10x into 6x + 4x, getting

x^2 + 6x + 4x + 24 = 0

Now we group the first two and the last two terms

x(x + 6) + 4(x + 6) = 0 Therefore,

(x+6)(x+4) = 0

For this to be true, at least one of the brackets needs to be 0.

For x + 6 = 0 we get x = -6

For x + 4 = 0 we get x = -4

Therefore, the set of solutions is S = {-6, -4}

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