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

Jun 17, 2015

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

#### Explanation:

$2 q + {q}^{2} = 15$
${q}^{2} + 2 q - 15 = 0$

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

Factorising by splitting the middle term

${q}^{2} + 5 q - 3 q - 15 = 0$
$q \left(q + 5\right) - 3 \left(q + 5\right) = 0$
$\left(q - 3\right) \left(q + 5\right) = 0$

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