# How do you solve x^2 + 7x - 44 = 0?

Apr 8, 2016

$x = - 11 , 4$

#### Explanation:

Begin with writing the equation into brackets.

$\left(x + a\right) \left(x + b\right) = 0$

You want to find $a$ and $b$ such that $a + b = 7$ and $a \cdot b = - 44$.

Through a process of trial and error, this gives $a = - 4$ and $b = 11$.

$\left(x - 4\right) \left(x + 11\right) = 0$

Anything multiplied by $0$ is $0$, meaning at least one of the brackets has to be equal to $0$. This actually gives two answers for $x$. Set each one equal to zero and then solve.

$x - 4 = 0$
$x = 4$

or

$x + 11 = 0$
$x = - 11$