# How do you solve using the completing the square method a^2+3a-40=0?

Aug 4, 2016

$a = 5$
$a = - 8$

#### Explanation:

Given -

${a}^{2} + 3 a - 40 = 0$

Take the constant term to the right

${a}^{2} + 3 a = 40$

Divide the coefficient of $x$ by 2. Square it and add the same to both sides

${a}^{2} + \frac{3}{2} x + \frac{9}{4} = 40 + \frac{9}{4}$

${\left(a + \frac{3}{2}\right)}^{2} = \frac{160 + 9}{4} = \frac{169}{4}$

$a + \frac{3}{2} = \pm \sqrt{\frac{169}{4}} = \pm \frac{13}{2}$

$a = \frac{13}{2} - \frac{3}{2} = \frac{10}{2} = 5$

$a = - \frac{13}{2} - \frac{3}{2} = - \frac{16}{2} = - 8$