How would I factor and solve 9x^2 - 25 = 0?

Question

 My alg 2 teacher doesn't really do a good job of explaining things, and I'm confused. Help?

Answer 1

Notice that both 9 and 25 are perfect squares.  That means we can factor them by their roots.

 

(3x-5)(3x+5)=0

 

You can double check those terms are correct by multiplying them back to see if you get back to the original.

9x^2 - 5x+5x -25=0

9x^2 -25 =0

 

Now set both terms equal to zero and solve.

 

3x-5 = 0

3x = 5

x = 5/3

 

3x+5 = 0

 3x = -5

x = -5/3