# How do you find the roots for x^2 + 24 = –11x?

Jun 5, 2015

First add $11 x$ to both sides to get

${x}^{2} + 11 x + 24 = 0$

$24 = 3 \times 8$ and $11 = 3 + 8$

So: ${x}^{2} + 11 x + 24 = \left(x + 3\right) \left(x + 8\right)$

This is based on the general observation that:

$\left(x + a\right) \left(x + b\right) = {x}^{2} + a x + b x + a b$

$= {x}^{2} + \left(a + b\right) x + a b$

Now $\left(x + 3\right) \left(x + 8\right) = 0$ when $x = - 3$ or $x = - 8$ so those are the roots of ${x}^{2} + 11 x + 24 = 0$