Quadratic Completing Square Worksheets Grade 9

1. Noah is constructing a rectangular sandbox for his community playground. The area of the sandbox is 66 square meters. The length of the sandbox is 1 meter more than twice its width. To order the correct amount of lumber for the frame, Noah needs to find the exact dimensions of the sandbox. Set up a quadratic equation for the width x and solve it by completing the square to determine the width and length of the sandbox.
2. A square is drawn on a coordinate plane with vertices at (0,0), (x,0), (x,x+6), and (0,x+6). The area of the square is 121 square units. Write a quadratic equation for x and solve it by completing the square.
3. x² + 16x + 21 = 0

…and 4 more problems

1. Emma is designing a square fountain for a park. She draws the fountain on a coordinate grid with one corner at the origin (0,0). The side length of the square is x meters. She then extends the fountain by adding a rectangular section along one side, increasing the total length by 9 meters, so the new shape is a rectangle with dimensions x by (x + 9). The area of this new rectangle is 112 square meters. Write a quadratic equation for this situation and solve for x by completing the square.
2. x² + 10x + 18 = 0
3. x² + 6x - 7 = 0

…and 4 more problems

1. A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 40 square meters, find the dimensions of the garden by setting up a quadratic equation and solving it by completing the square.
2. Sophia is designing a rectangular rooftop garden for an urban sustainability project. The length of the garden is 10 meters more than its width. The total area of the garden is 144 square meters. To determine if the design fits within the rooftop space, Sophia needs to find the exact dimensions. Set up a quadratic equation for the width (w) and solve it by completing the square to find the width and length of the garden.
3. Hana is designing a rectangular fish pond for her backyard. The area of the pond is 48 square meters. The length of the pond is 4 meters more than twice its width. She needs to find the exact dimensions to buy the correct liner. Set up a quadratic equation and solve it by completing the square to find the width and length of the pond.

…and 4 more problems