Question

Solve d^2 + 17d + 72 = 0 by factoring.
can someone show me how to do step by step please?

Answer 1

Alright so

ax^2 + bx + c = 0

You have to ask yourself what 2 numbers multiply to make 'c'....but also at the same time add to make 'b'

So for your question

\[\large d^2 + 17d + 72 = 0\]

what 2 numbers multiply to make 72..but at the same time add to make 17?

Answer 2

Okay, the constant term (no x in it) has to be a multiple of two numbers we call a and b.
So, 72 = a times b. The coefficient on the middle term (with only the first power of x has to be the sum of those two numbers. a + b = 17.

You have to consider the pairs of factors of 72 see which of them might be good for a and b. The pairs are 1 and 72, 2 and 36, 3 and 24, and so forth.

In reality I just look at it and see the answer, but with practice you can do the same thing with equations that factor with a and b being integers.

Answer 3

d^2+17d+72=0
(d+9)(d+8)=0
d=-9 or d=-8

Answer 4

Thank you both.