Question

49b^2 - 256 = 0 Solve, and show steps if you can!

Answer 1

Note that 49b^2 - 256 = 0 is the difference of two squares.  Thus, 49b^2 - 256 = 0 can be re-written as

(7b)^2 - 16^2 = 0, which factors into (7b+16)(7b-16)=0.

Solving for b:  7b+16=0 becomes b = -16/7, and
                        7b-16=0 becomes b = 16/7.

As expected, this 2nd order equation has 2 solutions.