Completing the Square

1
Completing the Square
(For help, go to Lessons 9-4 and 9-7.)
Find each square. 1. (d 4)2 2. (x 11)2 3. (k
8)2 Factor. 4. b2 10b 25 5. t2 14t
49 6. n2 18n 81
Check Skills Youll Need
10-5
2
Completing the Square
1. (d 4)2 d2 2d(4) 42 d2 8d 16 2.
(x 11)2 x2 2x(11) 112 x2 22x 121 3.
(k 8)2 k2 2k(8) 82 k2 16k 64 4. b2
10b 25 b2 2b(5) 52 (b 5)2 5. t2
14t 49 t2 2t(7) 72 (t 7)2 6. n2 18n
81 n2 2n(9) 92 (n 9)2
Solutions
10-5
3
Completing the Square
Find the value of c to complete the square for
x2 16x c.
The value of b in the expression x2 16x c is
16.
Quick Check
10-5
4
Completing the Square

• First, write the left side of the equation as a
  perfect square.
• X2 4x 12
• X2 4x 4 12 4
• Second, solve the equation by taking the square
  root of each side.
• (x 2)2 V16
• X 2 4
• X 4 2 and x -4 2
• X 6 and -2

5
Completing the Square

• Did you see that this can be factored using two
  binomials?.
• X2 4x 12
• X2 4x 12 0
• (x 6)( x 2) 0
• X 6 and -2

6
Completing the Square
Solve the equation x2 5x 50.
10-5
7
Completing the Square
(continued)
Step 2 Solve the equation.
Quick Check
10-5
8
Completing the Square
Solve x2 10x 16 0 by completing the
square. Round to the nearest hundredth.
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9
Completing the Square
(continued)
Step 2 Solve the equation.
Quick Check
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10
Completing the Square
ALGEBRA 1 LESSON 10-5
Suppose you wish to section off a soccer field
as shown in the diagram to run a variety of
practice drills. If the area of the field is 6000
yd2, what is the value of x?
10-5
11
Completing the Square
(continued)
Quick Check
The value of x is 40 yd.
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12
Completing the Square
Solve each equation by completing the square. If
necessary, round to the nearest hundredth.
1. x2 14x 43 2. 3x2 6x 24 0 3. 4x2
16x 8 40
9.45, 4.55
4, 2
5.46, 1.46
10-5