Completing the Square Worksheet
A Grade 10 Math worksheet focusing on completing the square to solve quadratic equations and rewrite quadratic expressions.
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Standards
Topics
Completing the Square
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Read each question carefully and show all your work. Complete the square to solve the quadratic equations or rewrite the expressions as indicated.
1. To complete the square for the expression x² + bx, you need to add the term (b/2)². This term makes the expression a perfect square trinomial, which can be factored as (x + b/2)². For the expression x² + 10x, the value of b is , and the term you need to add to complete the square is .
2. When completing the square for x² - 12x, the term to add is , resulting in the perfect square trinomial .
Rewrite the following quadratic expressions in the form (x + h)² + k by completing the square.
3. x² + 6x + 5
4. x² - 8x + 10
5. x² + 3x - 1
Solve the following quadratic equations by completing the square.
6. x² + 4x - 12 = 0
7. x² - 10x + 21 = 0
8. x² + 7x + 6 = 0
9. Which of the following is the correct step to complete the square for x² + 14x + ?
Add 7
Add 14
Add 49
Add 196
10. What are the solutions to x² - 6x + 5 = 0 after completing the square?
x = 1, x = 5
x = -1, x = -5
x = 2, x = 3
x = -2, x = 3
11. Completing the square can always be used to solve any quadratic equation.
True
False
12. When the coefficient of x² is not 1, you must divide the entire equation by that coefficient before completing the square.
True
False