Ashford University MAT 221
For this week’s Assignment we are given a word problem involving buried treasure and the use of the Pythagorean Theorem. We will use many different ways to attempt to factor down the three quadratic expressions which is in this problem. The problem is as, ““Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging.
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So looking at 225 we know that it has prime numbers 2 and 5 with a exponent of 2 next to the 2. So using our formula we will now use (2 + 1)(1 + 1) = (3)(2) = 6. Now when we’re looking at this there are many different possibilities of factors of 20. When looking at the term 20 of quadratic equation we can see that it could be ±1, ±2, ±4, ±5, ±10, and ±20. So now when we input our information into the equation we will use the formula of (ax + b)(cx + d) = 0. We will now use a as 1 and c as -1 and use our possibilities for b and d. I try to be as easy as possible in math so I will choose 4 and 5 as our b and d. We will now rewrite the formula to (1x + 4)(1x + 5) = 0, however when we use our FOIL method we will notice that it turns out to be x2 + 5x + 4x + 20 = x2 + 9x + 20 = 0 which in no shape or form is the same as x2 – 8x – 20 = 0 because of the negative numbers and the middle does not match. We will continue to input numbers into b and d to create the equation to match x2 – 8x – 20 = 0. With this being said we must also keep in mind that a and c will be multiplied to equal positive 1 and that the middle will create the sum of ad and bc to create a -8. We will also have to remember that b and d when multiplied will have to be the same as -20. When doing these types of problems in the homework I noticed that this is somewhat of a hit or miss as they say. After a few tries we will establish that (1x – 10)(1x + 2) = 0 will work and that a