find the root

Question

9x^2–1–(3x–2)^2=0

9x²–1–(3x–2)²=0

Answer 1

Simplify by expanding the square of the binomial, distributing the outside - sign, & collecting like terms.

Then it's just a matter of solving a quadratic equation; presumably you know a few methods.

 

The key step, I think, is the correctly square the binomial & distribute the - sign. Squaring every binomial always produces a trinomial.

Answer 2

9x²-1-(3x-2)² = 0

 

9x²-1-(9x²-12x+4) = 0

 

9x²-1-9x²+12x-4 = 0

 

               12x-5 = 0

 

               12x = 5

 

                  x = 5/12