4b²+32b+64 =?

Question

What is this equation? And how do I solve it?

Answer 1

Jazz;

Are we looking to solve or factor this?  As with your other question this is again a quadratic equation graphing to a parabola opening upward.  Let's see if this can be factored.

 

4b²+32b+64

All numbers are divisible by 4 so factor out the 4 giving...

4(b²+8b+16)

 

b²+8b+16 is further able to be factored as it is a perfect square ...  (b+4)² or (b+4)(b+4)

So we have..

 

4b²+32b+64 = 4(b+4)²  or, if you prefer   4(b+4)(b+4)

 

If you are supposed to solve this then, again, we normally see the equation in the form of

ax²+bx+c=0

In which case you would have

 

4(b+4)²=0

(b+4)²=0   when you divide both sides by 4

 The answer would be b=-4    This quadratic has a double root at x=-4

 

If you graph this you have a parabola with the vertex at (-4,0) opening upwards so the only place

the graph touches the x axis is at x=-4