b²x² + 2ax = x² + a²

b²x² - x² + 2ax - a² = 0

 (b²-1)x² + 2ax - a² = 0

We have to use the quadratic formula, but since the
quadratic formula contains the letters a and b, we
change the letters in the formula to capital letters:

x = 

Then A = b²-1, B = 2a, C = -a²

x = 

[Now we can see why they said "b does not equal 1" because the
denominator 2(b²-1) would be 0 if bcould equal 1, and we cannot
divide by 0].

x = 

x = 

x = 

x = 

x = 
 
x = 

x = 

x = 

There are two solutions, one using the + and one using the -

Solution 1:


x = 

Reverse the terms in the parentheses in the numerator:

x = 

Factor the denominator:

x = 

x = 

x = 

Solution 2:


x = 

Reverse the terms in the parentheses in the numerator:

x = 

Factor -1 out of the parentheses in the numerator:

x = 

x = 

Factor the denominator:

x = 

x = 

x = 

So the solutions are  and 

Edwin