Question

How do you solve `2q+q^2=15`?

Answer 1

`color(red)( q=3, q=-5`

Explanation:

`2q+q^2=15`
`q^2 + 2q-15=0`

We can first factorise this expression and then proceed towards finding the solution.

Factorising by splitting the middle term

`q^2 + 5q - 3q -15=0`
`q(q + 5) - 3(q +5)=0`
`(q - 3)(q +5)=0`

Equating with zero :
`q-3 = 0, q=3`
`q+5 = 0 , q=-5`
Thus the solutions are:
`color(red)( q=3, q=-5`