my best mistake this week was when I was reviewing how to solve equations by completing the square. When finding the zero pair for the equation instead of chopping the middle term in half and squaring that number, I only squared the middle term, ending up giving me the wrong answer. I did not check my answers and I ended up doing every question that involves completing the square this way. the correct way to solve by completing the square is finding the zero pair by dividing the middle term by 2 and squaring that number, solving from there.

My best mistake this week happened when we were learning to solve equations that are not factorable by completing the square. For the question + 4x + 6 = 0, I was able to properly complete the square, getting + 2 = 0. However, when it came to solving the equation I ended up with – 2. I thought it was weird that there was a negative radicand, but I left it like that thinking that was the final answer. I now know that when you end up with a negative radicand, the equation has no solution and that is a good answer. I also know how to be more efficient when answering these equations and as soon as I see a positive number on one side of the equation that is not in brackets, I will know the question will end with a negative radicand and therefore is not solvable.

My best mistake this week was on the question . I started by noticing each term had something in common and divided out the two. This is when I made the mistake of thinking the equation could be factored further. I did the box method because I couldn’t find anything that added to -2 and multiplied to 15. this was because the 15 was positive but I thought the signs did not matter and I put 2(x+3)(x-5). the correct way to factor this is leaving the answer once I realize it cannot be factored further. I will know this when I see that there is nothing that adds to the middle term and multiplies to the end term.

My best mistake this week was on the homework assignment for dividing radicals part two. When I was finding the conjugate on the questions that required it, I mistaken the conjugate for the opposite of the expression shown on the denominator. For example, if the denominator was I would write the conjugate as which does not work out since you cannot take the square root of a negative number. Instead, the correct conjugate for is .

This week I did not make any exceptionally good mistakes to learn from, except when I was adding and subtracting radicals together, I forgot that you need a common radicand. One specific question I did this on was a question from the workbook’s first assignment

+

since there was not an obvious common radicand, I did not remember we needed one and I treated the addition as you would multiplication and just added across giving me

which was not the answer to the question. Looking back, it was a pretty obvious mistake and hopefully one I will not make again. I will make sure of this by taking my time to carefully read the question, write out all my steps, and check the answer in the answer key to make sure I did everything right.

The correct way to do this question is by taking the two numbers and turning them into mixed radicals, so that the radicands have a common number. once you simplify the radicals by turning them into mixed radicals, you should have the equation

+

Once you have the common radicands, you are then able to add across giving you the answer of:

My best mistake that I learned from this week was during the skills check on #4 question 3 where we were supposed to simplify the expression and write it as a power with a positive exponent and then as a radical.

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I did not remember that when two equations are in brackets together you multiply everything in the brackets. I only multiplied the radicands with each other and instead of multiplying the two index’s, I added them. Now I know that when two radicals are in separate sets of brackets next to each other, you multiply the radicands with each other and you multiply the index’s with each other to get the answer.

For this weeks writing prompt, I have chose a quote on Ms. Burton’s wall of quotes that I resonate with the most, impacting my perspective of Pre Calculus 11. The quote I have chosen is “It’s not failure because I haven’t given up yet”. This impacts me because it is true in the sense that I may not understand something immediately and that’s ok because as long as I keep trying, it is not failure and it will eventually become success. If I give up on something just because I make a mistake, it means that I will never get to learn from the mistake and get to improve. No matter what happens it is important not to give up because only then is it failure, if you don’t give up and it still does not work, at least you can know you tried your hardest.