# How do you solve using the completing the square method 8x^2 – 80x = –24?

Apr 12, 2016

$x = 5 + \sqrt{22}$ or $x = 5 - \sqrt{22}$

#### Explanation:

In $8 {x}^{2} - 80 x = - 24$, we have $8$ as common factor. Hence dividing by $8$, we get ${x}^{2} - 10 x = - 3$.

We can make the Left Hand Side of ${x}^{2} - 10 x$, a complete square by comparing it with ${\left(x - a\right)}^{2} = {x}^{2} - 2 a x + {a}^{2}$ i.e. by adding square of half the coefficient of $x$.

As coefficient of $x$ is $- 10$, we need to add ${\left(- \frac{10}{2}\right)}^{2} = 25$, to each side and then we have

${x}^{2} - 10 x + 25 = 25 - 3 = 22$

or ${\left(x - 5\right)}^{2} = {\left(\sqrt{22}\right)}^{2}$

Hence either $x - 5 = \sqrt{22}$ or $x - 5 = - \sqrt{22}$ i.e.

$x = 5 + \sqrt{22}$ or $x = 5 - \sqrt{22}$