How do you solve x^2 + 16x = 0 by completing the square?

May 26, 2015

If ${x}^{2} + 16 x$ are the first two terms of an squared expression
${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$
then $a = 8$

${x}^{2} + 16 x = 0$
can be written as
${x}^{2} + 16 x + {8}^{2} = {8}^{2}$

#(x+8)^2 = 64

Taking the square root
$x + 8 = \pm 8$

and
$x = 0$ or $x = 16$