Edmentum Integrated Math2 Unit 4 Activity: Solving Quadratic Equations

Type the correct answer in each box. Write your answers in decimal form, rounded to the nearest tenth, if necessary. Type the solution with the smaller value in the first blank.

(Hint: to complete your calculations, you may need to use mental math.)

Select and use the most direct method to solve 2x(x + 1.5) = -1.

Type the correct answer in the box.
Solve this equation using the most direct method:

3x(x + 6) = -10

Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using the ± symbol.

Describe and justify the methods you used to solve the quadratic equations in parts A and B.

Ann works for a city’s parks and recreation department. She is looking for some commercial land to rezone for recreational use and has found two possible options.

Part A
Ann’s first option is a plot of land adjacent to a current park. The current park is a square, and the addition will increase the width by 200 meters to give the expanded park a total area of 166,400 square meters. This equation represents the area of the first option, where x is the side length of the current square park:

x2 + 200x = 166,400.

Use the most direct method to solve this equation and find the side length of the current square park. Explain your reasoning for both the solving process and the solution.

Ann’s second option is rezoning two separate plots of land. One is square, and the other is triangular with an area of 32,500 square meters. For this second option, the total area would be 76,600 square meters, which can be represented by this equation, where x is the side length of the square park:

x2 + 32,500 = 76,600.

Use the most direct method to solve this equation and find the side length of the square-shaped park. Explain your reasoning for both the solving process and the solution.

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