Completing the Square Objectives n Solve quadratic equations

Completing the Square

Objectives n Solve quadratic equations by completing the square.

In the previous lesson, you solved quadratic equations by isolating x 2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When a trinomial is a perfect square, there is a relationship between the coefficient of the x-term and the constant term. x 2 + 6 x + 9 x 2 – 8 x + 16 Divide the coefficient of the x-term by 2, then square the result to get the constant term.

An expression in the form x 2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x 2 + bx to form a trinomial that is a perfect square. This is called completing the square.

Examples Complete the square to form a perfect square trinomial. 1. x 2 + 2 x + 2. x 2 – 6 x +

Complete the square to form a perfect square trinomial. 3. x 2 + 12 x + 4. x 2 – 5 x +

Solving a Quadratic Equation by Completing the Square

Examples Solve by completing the square. 5. x 2 + 16 x = – 15 6. x 2 – 4 x – 6 = 0

Solve by completing the square. 7. x 2 + 10 x = – 9 8. t 2 – 8 t – 5 = 0

Examples Solve by completing the square. 10. 5 x 2 + 19 x = 4 9. – 3 x 2 + 12 x – 15 = 0

Solve by completing the square. 11. 3 x 2 – 5 x – 2 = 0 12. 4 t 2 – 4 t + 9 = 0

Homework n Worksheet