Question

factorize x^2-34x-573=0

Answer 1

you need two numbers that multiply to -573 and add up to -34 (i don't think there are any factors that work)
i think it's easier to do this using complete the square method.
x^2 - 34x = 573
(x^2-34x + 289) = 573 +289
(x-17)^2 = 862
x-17 = + sqrt (862) or - sqrt(862)
so x = sqrt(862) + 17 or -sqrt(862) + 17