**Pythagorean Quadratic**

Read the following instructions in order to complete his assignment and review the example of how to complete the math required for this assignment, and review the example of how to complete the math required for this assignment:

- Read problem 98 on page 371 of
*Elementary and Intermediate Algebra*. Along with factoring, this problem also requires the use of the Pythagorean Theorem to solve it.

**Problem #98**

**Buried Treasure**. Ahmed has half of a treasure map, which indicates that the treasure is buried in 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 go 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*?

- On your scratch paper, draw a diagram which includes the location of Castle Rock and the dimensions of a triangle with the given number of paces. Seeing the relationship of the sides and where the right angle is will help you know how to apply the Theorem. You may include the diagram in your paper but are not required to do so.
- Write the equation first by inserting the given binomials into the Pythagorean Theorem. Once you have your equation written, solve it using the methods from section 5.6 of
*Elementary and Intermediate Algebra*. Show all steps and explain what you are doing as you go.

**5.6: Solving Quadratic Equations by Factoring**

**The Zero Factor Property: **In this chapter you learned to factor polynomials such as x^{2}+x-6. The equation x^{2}+x-6=0 is called a *quadratic equation*.

**Quadratic Equation:** If a, b, and c are real numbers with a≠0, then ax^{2}+bx+c=0 is called a quadratic equation.

**The zero factor property:** The equation a•b=0 is equivalent to a=0 or b=0.

** **

**Strategy for solving an Equation by Factoring**

1. Rewrite the equation with 0 on one side.

2. Factor the other side completely.

3. Use the zero factor property to get simple linear equations.

4. Solve the linear equations.

5. Check the answer in the original equation.

6. State the solution(s) to the original equation.

** **

- Write a two- to three-page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning. In the body of your essay, do the following:
- Demonstrate your solution to the above problem, making sure to include all mathematical work and an explanation for each step.
- Explain which solution to the equation is the best solution and why it is the best solution. How many steps is the map from Castle Rock?
- Incorporate the following four math vocabulary words into your writing. Use
**bold**font to emphasize these words in your writing (Do not write definitions for the words; use them appropriately in sentences describing your math work): - Quadratic
- Zero factor
- Pythagorean Theorem
- Compound equation

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