How do you solve a^2 - 4a = 32?

Apr 16, 2018

$a = 8 , a = - 4$

Explanation:

Minus $32$

$\to {a}^{2} - 4 a - 32$

List the factors of $32$:

$1$ and $32$
$2$ and $16$
$4$ and $8$

As you can see, we can make $- 4$ from $8$ and $4$

$\to \left(a - 8\right) \left(a + 4\right)$

Solve:

$a - 8 = 0$

$a = 8$

$a + 4 = 0$

$a = - 4$

Therefore $a = 8 , a = - 4$

We can always check the answer:

$a = 8$

${8}^{2} - \left(4 \times 8\right) = 64 - 32 = 32$

$a = - 4$

${\left(- 4\right)}^{2} - \left(- 4 \times 4\right) = 16 + 16 = 32$

Hence $a = 8 , a = - 4$ is correct