Pythagorean Theorem

The assignment for the week is on page 371 number 98. We will be using Pythagorean Theorem, quadratic, zero factor, and compound equation, to solve this equation. We will explain step by step to solve how many paces to reach Castle Rock for Ahmed and Vanessa had to accomplish to meet there goal. 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. What is x (Dugoploski, 2012)? With the information we know that Vanessa must walk North x paces, then 2x + 4 paces to the East. We do not know which direction Ahmed must go, however, we assume that they will end up in the same location. Using a piece of paper, I drew the triangle and it is right triangle. Now I can use the Pythagorean Theorem to help solve for x. The Pythagorean Theorem is a^2 + b^2 = c^2. Letting a = x, b= 2x+4, and c = 2x + 6. a^2 + b^2 = c^2 Pythagorean Theorem x^2 + (2x+4)^2 = (2x+6)^2 Putting the binomials into the Pythagorean Theorem. x^2 + 4x^2 + 16x +16 = 4x^2 + 24x + 36 Binomials squared. This is 4x^2 on both sides of the equation which can be (4x)^2 subtract out first leaving the equation to be. x^2 + 16x + 16 = 24x +36 subtract (4x)^2 Next we should subtract 16x from both sides of the equation, which then leaves us with. x^2 + 16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of

x^2 – 20 = 8x. Finally we need to subtract 8x from both sides to get x^2 – 8x – 20 = 0 Now we have a quadratic equation to solve by factoring and using the zero factor.
(x-)(x+) = 0. Since the coefficient of x^2 is 1 we can start with a pair of parenthesis with an x in each. Since the 20 is negative we know there