X^2 - 24x+143=0 Factor and solve

x = 13 and x = 11

To factor this equation, we find the factors of 143, which are 1, 11, 13 and 143, and this case we also include their negatives (-1, - 11, - 13 and - 143). We then see which ones of those add up to - 24, and those two are - 11 and - 13.

Using those, we can factor the equation into (x-13) (x-11) = 0

(To check this, we can see that the first two terms multiply to x^2, the middle two terms multiple to - 13x and - 11x, which simplify to - 24x, and the last two terms multiply to 143, so it is indeed the same as the original equation)

Using the Zero Produce Property, we can split the factored equation into x-13 = 0 and x - 11 = 0, which gives us x = 11 and x = 13