Page 712 - Algebra 1

L E S S O N Solving Quadratic Equations by
104
Completing the Square
Warm Up
1. Vocabulary A is a trinomial that is the square of a binomial. (60)
Simplify.
2. (8 ) (3) 3
3. (12 ) - 5 (4) 3
5.x2 -18x+81=0 (98)
_2 _2
Solve.
4.x2 +6x+9=0
(98)
New Concepts The product of a binomial square is a perfect-square trinomial.
Binomial Square (x-7)2
Perfect-Square Trinomial x2 -14x+49
x2 +6x+9
(x+3)2
Completing the square is a process used to form a perfect-square trinomial.
Hint
The last term of the binomial is doubled to get the coefficient of
the middle term of the trinomial and squared to get the last term of the trinomial.
Completing the Square
2 _b 2
Complete the square of x + bx by adding (2 ) to the expression.
x2 + bx + x2 + bx +
_2 x2 +bx+(b ) 22
( x + _b ) 2 2
_b 2 (2)
Example: x2 + 6x + x2 + 6x +
x2 +6x+(3)2 x2 +6x+9
(x + 3)2
_6 2 (2)
Example
1
Completing the Square
Complete the square. x2 + 8x
SOLUTION
x2 + 8x +
Online Connection www.SaxonMathResources.com
2 _82 x +8x+(2)
x2 + 8x + (4)2 x2 + 8x + 16
Addthesquareof8dividedby2.
Simplify the fraction. Simplify.
Lesson 104 697