Completing the Square

Objectives 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 + 6x + 9 x 2 – 8x + 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 + 2x + 2. x 2 – 6x +

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

Solving a Quadratic Equation by Completing the Square

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

Solve by completing the square. 7. x x = –98. t 2 – 8t – 5 = 0

Examples Solve by completing the square. 9. –3x x – 15 = x x = 4

Solve by completing the square x 2 – 5x – 2 = t 2 – 4t + 9 = 0

Homework Worksheet