9x^2-256=0 using the quadratic formula

Question

step-by-step 

im confused when i get down to ±√9216/18

Answer 1

Inside (b2 -4ac) which it comes out to be 9216, is perfect square.  Since b² is 0, all you have is -4ac as (-4)(9)(-256) and you can distribute two of negative signs and make them all three numbers +.  So you can say that (4)(9)(256).  From all three numbers, each numbers are all perfect squares.  Square root of 4 is 2, 9 is 3, and 256 is 16.  So, you are left with 2, 3, 16.  As you multiply these three numbers, you will get 96 which is square root of 9216.

 

If you factor this (difference of square) as factor form it looks like this: (3x+16)(3x-16) since 9 is perfect square and 256 is perfect square.

 

If you ever get confused with big number like this, break them down.  Remember, (b² - 4ac) must be 0 or greater.  In another words, (b² - 4ac) cannot be negative.

 

Good Luck to you.

Answer 2

We have a = 9, b = 0, and c = -256, so 

x = [-b ± √(b^2 - 4ac)]/2a 

   = [-0 ± √(0^2 - 4(9)(-256))]/2(9)

   = ±√(9216)/18 

   = ±96/18 

   = ±16/3

 

You were almost there. You just had to see that 9216 is a perfect square.