TakeSquare
out your homework.
8-8 Completing -the
Warm Up
Simplify.
Write
your name at the TOP of page 453.
- Finish your warm-up and place it on
my laptop.
- Pick up your controller and turn it
on.
1.
2.
3.
4.
Solve by factoring.
5. x2 + 8x + 16 = 0
Holt McDougal Algebra 1
x = –4
19
8-8 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.
8-8 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
8-8 Completing the Square
Example 1: Completing the Square
Complete the square to form a perfect square
trinomial.
A. x2 + 2x +
x2 + 2x + 1
Holt McDougal Algebra 1
B. x2 – 6x +
x2 – 6x + 9
8-8 Completing the Square
Check It Out! Example 1
Complete the square to form a perfect square
trinomial.
a. x2 + 12x +
x2 + 12x + 36
Holt McDougal Algebra 1
b. x2 – 5x +
x2 – 5x +
8-8 Completing the Square
Check It Out! Example 1
Complete the square to form a perfect square
trinomial.
c. 8x + x2 +
x2 + 8x + 16
Holt McDougal Algebra 1
8-8 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
8-8 Completing the Square
Solving a Quadratic Equation by Completing the Square
Holt McDougal Algebra 1
8-8 Completing the Square
Example 2A: Solving x2 +bx = c by Completing the
Square
Solve by completing the square. Check your answer.
x2 + 16x = –15
{-15,-1}
Holt McDougal Algebra 1
8-8 Completing the Square
Example 2B: Solving x2 +bx = c
Solve by completing the square. Write your answer
in simplest radical form. Check your answer.
x2 – 4x – 6 = 0
2 − 10, 2 + 10
Holt McDougal Algebra 1
8-8 Completing the Square
Check It Out! Example 2a
Solve by completing the square. Check your answer.
x2 + 10x = –9
{-9,-1}
Plug in the greater value
Holt McDougal Algebra 1
8-8 Completing the Square
Check It Out! Example 2b
Solve by completing the square. Write your answer
in simplest radical form. Check your answer.
t2 – 8t – 5 = 0
4 − 21, 4 + 21
Holt McDougal Algebra 1
8-8 Completing the Square
Example 3A: Solving ax2 + bx = c by Completing the
Square
Solve by completing the square.
–3x2 + 12x – 15 = 0
There is no real number whose square is
negative, so there are no real solutions.
Holt McDougal Algebra 1
8-8 Completing the Square
Check It Out! Example 3b
Solve by completing the square.
4t2 – 4t + 9 = 0
There is no real number whose square is negative, so
there are no real solutions.
Holt McDougal Algebra 1
8-8 Completing the Square
Example 3B: Solving ax2 + bx = c by Completing the
Square
Solve by completing the square.
5x2 + 19x = 4
1
−4,
5
Plug in the negative value
Holt McDougal Algebra 1
8-8 Completing the Square
Check It Out! Example 3a
Solve by completing the square.
3x2 – 5x – 2 = 0
1
− ,2
3
Plug in the sum of the values
as an improper fraction.
Holt McDougal Algebra 1
8-8 Completing the Square
Example 4: Problem-Solving Application
A rectangular room has an area of 195
square feet. Its width is 2 feet shorter than
its length. Find the dimensions of the room.
Round to the nearest hundredth of a foot, if
necessary.
Negative numbers are not reasonable for length, so
x = 13 is the only solution that makes sense.
The width is 13 feet, and the length is 13 + 2, or
15, feet.
Holt McDougal Algebra 1
8-8 Completing the Square
Check It Out! Example 4
An architect designs a rectangular room
with an area of 400 ft2. The length is to
be 8 ft longer than the width. Find the
dimensions of the room. Round your
answers to the nearest tenth of a foot.
The width is approximately16.4 feet, and the length
is 16.4 + 8, or approximately 24.4, feet.
Holt McDougal Algebra 1
8-8 Completing the Square
Lesson Quiz: Part I
Complete the square to form a perfect square
trinomial.
1. x2 +11x +
2. x2 – 18x +
81
Solve by completing the square.
3. x2 – 2x – 1 = 0
4. 3x2 + 6x = 144
5. 4x2 + 44x = 23
Holt McDougal Algebra 1
6, –8
8-8 Completing the Square
Lesson Quiz: Part II
6. Dymond is painting a rectangular banner for a
football game. She has enough paint to cover
120 ft2. She wants the length of the banner to be
7 ft longer than the width. What dimensions
should Dymond use for the banner?
8 feet by 15 feet
Holt McDougal Algebra 1