The Pythagorean Theorem was styled after Pythagoras, who was a well-known Greek philosopher and mathematician, and the Pythagorean Theorem is one of the first theorems recognized in ancient human development. “The Pythagorean theorem states that in any right triangle the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse” (Dugopolski, 2012). Based on these grounds, many builders from assorting times throughout history have utilized this theorem to guarantee that their infrastructures were positioned with right angles. In this assignment, we will use the example of locating a treasure using two varying treasure maps as the two points needed to regulate how many paces are needed to find the precise location to start digging for treasure. For this assignment, we are given instructions to solve problem number 98 from page 371 in Elementary and Intermediate Algebra, which states that Ahmed’s treasure map describes that the treasure can be found 2x +6 steps from Castle Rock and Vanessa’s half indicates to walk x steps heading north, then 2x + 4 steps toward the east (Dugopolski, 2012). The Pythagorean Theorem is needed to figure out what variable x would be if they were to join forces and integrate their data. The Pythagorean Theorem designates that a right triangle has legs with the length of a and b and the longest side of the triangle, the “hypotenuse” as the length of c. Thus, the relationship with these lengths is the short equation of a2 + b2 = c2 (Dugopolski, 2012).

Let a = x

Let b = 2x + 4

Let c = 2x + 6 a2 + (2x + 4)2 = (2x +6)2 Plug the binomials into the Pythagorean Theorem

PYTHAGOREAN QUADRATIC 3 a2 + 4x2 +16x +16 = 4x2 + 24x + 36 The binominal are now squared and the 4x2 is then -4x2 -4x2 subtracted from both sides of the equation a2 + 16x +16 = 24x + 36 Now the 24x is subtracted from both sides of the

-24x -24x equation. a2 - 8x +16 = 36 subtract 36 from both sides -36 -36 a2 - 8x -20 = 0 Remaining is a quadratic equation to solve by factoring and using the zero factor

Two factors of -20 that adds up to -8 are needed.

-1,20; 1,-20; -4,5; 4,-5; -2,10; 2,-10 factors 2