# How do you factor and solve x^2+5x-24=0?

May 31, 2015

Look for a pair of factors of $24$ whose difference is $5$.

$24 = 8 \times 3$ and $5 = 8 - 3$

So

${x}^{2} + 5 x - 24$

$= {x}^{2} + \left(8 - 3\right) x - \left(8 \times 3\right)$

$= \left(x + 8\right) \left(x - 3\right)$

So the solutions of ${x}^{2} + 5 x - 24 = 0$ are $x = - 8$ and $x = 3$