Holt McDougal Algebra 1

9-8 Completing the Square

Solve quadratic equations by completing the square.

Objective

Holt McDougal Algebra 1

9-8 Completing the Square

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 + 9 x2 – 8x + 16 Divide the coefficient of the x-term by 2, then square the result to get the constant term.

Holt McDougal Algebra 1

9-8 Completing the 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.

Holt McDougal Algebra 1

9-8 Completing the Square

Example 1: Completing the Square

Complete the square to form a perfect square trinomial.

A. x2 + 2x + B. x2 – 6x +

Holt McDougal Algebra 1

9-8 Completing the Square

Example 2

Complete the square to form a perfect square trinomial.

a. x2 + 12x + b. x2 – 5x +

Holt McDougal Algebra 1

9-8 Completing the Square

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.

Holt McDougal Algebra 1

9-8 Completing the Square

Solving a Quadratic Equation by Completing the Square

Holt McDougal Algebra 1

9-8 Completing the Square

Example 3

Solve by completing the square. Check your answer.

x2 + 16x = –15

Holt McDougal Algebra 1

9-8 Completing the Square

Example 4

Solve by completing the square. Check your answer.

x2 + 10x = –9

Holt McDougal Algebra 1

9-8 Completing the Square

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

Practice