How do you solve 30a² plus a equals 20?

Answer 1

30a2 + a = 20

∴ 30a2 + a - 20 = 0

To factor this out, find two values whose sum is equal to the coefficient of the middle term, and whose product is equal to the product of the first and last terms' coefficients:

x + y = 1

xy = 600

Because x and y are so close together, we know that they'll be fairly close to the square root of 600, which is about 24.4949. So let's try 24 and 25:

24 × 25 = 600

bingo. So we'll take those two terms, and use them in our original equation, replacing the middle term with each of them (keeping in mind that their sum must equal the middle term):

∴ 30a2 -24a + 25a - 20 = 0

∴ 6a(5a - 4) + 5(5a - 4) = 0

∴ (6a + 5)(5a - 4) = 0

∴ a ∈ {-5/6, 4/5}