How does completing the trinomial square help you solve an equation by using the principle of square root?

Can you consider the following and demonstrate the concept?

x^2 + 4x = 21

Question

How does completing the trinomial square help you solve an equation by using the principle of square root?

Can you consider the following and demonstrate the concept?

x^2 + 4x =  21

anonymous · Answer

$$x^2+4x=21$$
$$x^2+4x+4=25$$
$$(x+4)^2=25$$
$$x+4=4$$
or
$$x+4=-5$$

anonymous · Answer

the picture goes like this.  draw a square with side x.  its area is $$x^2$$
attach to two sides a rectangle with side 2.  each has area $$2x$$ for a total of $$x^2+4x$$
this picture is not a square.  to make it a square you have to actually 
complete the square, but adding a little $$2\times 2$$ square for the piece that is missing.

anonymous · Answer

since that little square has area 4 you now have a total of 21+4 = 25 and you have a '
perfect square" whose sides are now $$x+2$$

myininaya · Answer

attachment

anonymous · Answer

here is a nice illustration of what i meant http://www.google.com/imgres?imgurl=http://www.helpalgebra.com/articles/images/csa5.gif&imgrefurl=http://www.helpalgebra.com/articles/completingthesquare.htm&usg=__JKUyjfzmv82JSJ-8_UKbwGL33rs=&h=265&w=273&sz=3&hl=en&start=0&sig2=AA_ZOZmz-ML9NmLwSKNaFw&zoom=1&tbnid=y_uiDGxEULpUCM:&tbnh=151&tbnw=156&ei=uPrJTab0G-WV0QGdzKXPBw&prev=/search%3Fq%3Dpicture%2Bof%2Bcompleting%2Bthe%2Bsquare%26hl%3Den%26client%3Dubuntu%26hs%3Deof%26sa%3DX%26channel%3Dfs%26biw%3D1211%26bih%3D798%26tbm%3Disch%26prmd%3Divns&itbs=1&iact=hc&vpx=642&vpy=258&dur=5668&hovh=212&hovw=218&tx=126&ty=116&page=1&ndsp=24&ved=1t:429,r:9,s:0

anonymous · Answer

oops guess that didn't work.

anonymous · Answer

lol....I thought what the heck is going on?