Page 56 - Math Course 3 (Book 1)

Solving Quadratic Equations

Mo. 2

Lesson 3 Let’s Begin

KEY CONCEPTS:
1. Solve quadratic equations by finding the Irrational Roots
square root.
2. Solve quadratic equations by completing the Example
square.

2
Solve x + 6x + 9 = 5 by taking the square root of
MO. 2 - L3a each side. Round to the nearest tenth if necessary.

2
Quadratic Equations: x + 6x + 9 = 5 Original equation
Finding the Square Root (x + 3) = 5 x + 6x + 9 is a perfect square
2
2
trinomial.
Vocabulary A-Z = 5 Take the square root of each
2
(x + 3)
Let us learn some vocabulary side.

| x + 3 | = 5 Simplify.

x + 3 = ± 5 Definition of absolute value.
completing the square
To make any quadratic expression a perfect Solve x + 6x + 9 = 5 by taking the square root of
2
square, a method called completing the square each side. Round to the nearest tenth if necessary.
may be used.
x + 3 – 3 = ± – 3 Subtract 3 from each side.
5
2
2
(x + 6) = x + 2(6)(x) + 6 2
x = –3 ± 5 Simplify.
2
= x + 12x + 36
Use a calculator to evaluate each value of x.
2
12 6 2 x = –3 + 5 or x = –3 – 5
2 ≈ –0.8 ≈ –5.2
2
Notice that one half of 12 is 6 and 6 is 36
Answer The solution set is {–5.2, –0.8}.

Complete the Square

Example

Find the value of c that makes x – 12x + c a perfect square.
2
Method 1 Use algebra tiles.

Arrange the tiles for
x – 12x + c so that the To make the figure a
2
two sides of the figure are square, add 36 positive
congruent. 1-tiles.
2
x – 12x + 36 is a perfect square.
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