# How do you solve  h^2 + 10h = -21?

Jun 24, 2015

The solutions are
 color(green)( h = -3 , h = -7

#### Explanation:

${h}^{2} + 10 h + 21 = 0$

Here, we can first factorise the expression and then find the solutions:

Factorising by splitting middle term:

${h}^{2} + 10 h + 21 = 0$
${h}^{2} + \textcolor{g r e e n}{3 h + 7 h} + 21 = 0$
$h \left(h + 3\right) + 7 \left(h + 3\right) = 0$
$\left(h + 3\right) \left(h + 7\right) = 0$
Equating the factors with zero to obtain solutions:
 h+3 = 0 ,color(green)( h=-3
 h+7 = 0 , color(green)(h=-7