The first time I tried this problem, I found it challenging because of the sheer amount of steps that were involved in the problem. While working through it, I made sure to work slowly to avoid any possible mistakes that could occur.

However, while I was simplifying terms, I accidentally forgot to subtract x from the left side, giving me 2x – 3 = 4√x + 2 instead of x – 3 = 4√x + 2. This resulted in me struggling when it came to factoring the trinomial, as I had incorrect values that I was trying to find factors for.

Eventually, I figured out what I had done wrong after a classmate let me know that something was wrong with the equation. I looked through every step I had done up to that point and discovered my error of forgetting to subtract x. Once I had made the appropriate changes, I was able to go through the rest of the steps easily and solve the equation.

To be able to solve this problem, I needed to use skills that we had been practicing all throughout unit one. The overall problem was solving for x and determining any restrictions or extraneous solutions. I had to isolate one radical on one side while using FOIL on the other side of the equation. The problem also involved simplifying terms and factoring trinomials, which I did by using the Zero Product Property. To determine the extraneous solutions, I simply plugged in the answers I had gotten for x into the equation to see whether they were correct, which -1 was not. To determine restrictions, I took the radicands, turned them into inequality equations and solved for x. As -3/2 was a greater number than -2, it was used as the restriction because any number greater than -3/2 will automatically be greater than -2.

Next time I encounter a difficult equation, I might try looking over previous steps before moving on to the next step to ensure that I haven’t made any errors along the way.