Question

How do you solve `a^2+a-30=0`?

Answer 1

Solve `y = x^2 + x - 30 = 0`

Explanation:

`y = x^2 + x - 30 = 0`
Find 2 numbers knowing sum (-1) and product (-30). Roots have opposite signs.
Factor pairs of (-30) --> ....(-3, 10)(-5, 6). This sum is 1 = b.
Then the 2 real roots are the opposite: `5 and -6`

Answer 2

Factor the trinomial into two binomials. Set each binomial equal to zero and solve for `a`.

Explanation:

`a^2+a-30=0`

Find two numbers that when added equal `1`, and when multiplied equal `-30`.

The numbers `-5` and `6` fit the pattern.

`a^2+a-30=0` =

`(a-5)(a+6)=0`

Set `(a-5)` equal to zero and solve for `a`.

`a-5=0`

`a=5`

Set `(a+6)` equal to zero and solve for `a`.

`a+6=0`

`a=-6`

`a=-6, 5`