Complete the Square Worksheets Grade 9

1. x² + 12x + 29 = (x + ?)² + ?
2. x² - 6x + 5 = (x - ?)² - 4
3. A rectangular garden has a length that is 2 meters more than its width. If the area of the garden is 120 square meters, find the dimensions of the garden by completing the square.

…and 6 more problems

1. Kaia is designing a rectangular meditation garden. The length of the garden is 14 meters more than its width. The area of the garden is 207 square meters. Write the expression for the area in the form (w + h)^2 + k, where w is the width of the garden, and then determine the width of the garden.
2. Isabella is designing a rectangular patio. The length of the patio is 14 meters more than its width. The area of the patio is 207 square meters. By completing the square, express the relationship in the form (w + h)² = k, where w is the width of the patio in meters. What is the value of k?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (x,0), and (0,6). The hypotenuse has length 10 units. Using the Pythagorean theorem, find the value of x.

…and 5 more problems

1. A rectangular garden has a length that is 6 meters more than its width. If the area of the garden is 135 square meters, what is the length of the garden in meters?
2. Emma is analyzing the graph of the quadratic function f(x) = x² + 10x + 15. She notices that the parabola can be rewritten in vertex form by completing the square. What is the vertex of the parabola?
3. The quadratic expression x² + 14x + k is a perfect square trinomial. What is the value of k?

…and 5 more problems