1. Objective
Solve quadratic equations by completing the square.

2. In the previous lesson, you solved quadratic equations by isolating x2 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.
X2 + 6x x2 – 8x + 16
Divide the coefficient of the x-term by 2, then square the result to get the constant term.

3. An expression in the form x2 + bx is not a perfect square
An expression in the form x2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x2 + bx to form a trinomial that is a perfect square. This is called completing the square.

4. Example 1: Completing the Square
Complete the square to form a perfect square trinomial.
A. x2 + 2x +
B. x2 – 6x +

5. Example 2
Complete the square to form a perfect square trinomial.
a. x2 + 12x +
b. x2 – 5x +

6. To solve a quadratic equation in the form x2 + bx = c, first complete the square of x2 + bx. Then you can solve using square roots.

7. Solving a Quadratic Equation by Completing the Square

8. Example 3
Solve by completing the square. Check your answer.
x2 + 16x = –15

9. Example 4
Solve by completing the square. Check your answer.
x2 + 10x = –9

10. Practice
Complete the square to form a perfect square trinomial.
1. x2 +11x +
2. x2 – 18x +
Solve by completing the square.
3. x2 + 6x = 144
4. x2 + 8x = 23