Question

Solve each of the following equation by using the method of completing the square:
$x^2-8x-2=0$ ?

Answer 1

We will use the difference of squares identity ,which can be written

$a^2-b^2=(a-b)(a+b)$ with

$a=(x+4)$ and

$b=\sqrt{14}$ as follows:

$0=x^2+8x+2=(x+4{)}^2-16+2$

$=(x+4)2-\left(\sqrt{14}\right)2$

$=\left(\right(x+4)-\sqrt{14})\left(\right(x+4)+\sqrt{14})$

$=(x+4-\sqrt{14})\left(\right(x+4+\sqrt{14})$

Hence:$x=-4\pm \sqrt{14}$

$x=\sqrt{14-4}$ OR

$x=-\sqrt{14-4}$

$x=-0.258$ OR

$x=-7.742$