Transcript Slide 1

9-8 Completing the Square
Objective
Solve quadratic equations by
completing the square.
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
Holt McDougal Algebra 1
x2 – 8x + 16
Divide the coefficient of
the x-term by 2, then
square the result to get
the constant term.
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 +
Holt McDougal Algebra 1
B. x2 – 6x +
9-8 Completing the Square
Example 2
Complete the square to form a perfect square
trinomial.
a. x2 + 12x +
Holt McDougal Algebra 1
b. x2 – 5x +
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
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
Holt McDougal Algebra 1