Beginning Algebra, 11th Edition

Rewriting a Quadratic Equation before Solving

Solve

Write the given equation in standard form as

Quadratic formula

Substitute

and

Simplify the radicand.

Factor to write in lowest terms.

x= 1  22 Divide out the common factor.

x=

2 A 1  22 B

2

x = 28 = 24 # 22 = 222

2  222

2

x=

2  28

2

b=-2, c=-1.

a=1,

x=

- 1 - 22  21 - 222 - 41121 - 12

2112

x=

• b 2 b^2 - 4 ac
  2 a

x^2 - 2 x- 1 =0.

x^2 = 2 x+1.

EXAMPLE 3

570 CHAPTER 9 Quadratic Equations

NOW TRY
EXERCISE 3
Solve x^2 + 2 = 6 x.

NOW TRY ANSWERS

3. E 3  27 F

Be careful

substituting

the negative

values.

Factor first.

Then divide out

the common

factor.

The solution set is E 1  22 F. NOW TRY

OBJECTIVE 3 Solve quadratic equations with only one solution.In the

quadratic formula, the quantity under the radical,

Discriminant

is called the discriminant.When the discriminant for equals 0

and a, b, and care integers, the equation has just one rational number solution.

Furthermore, the trinomial ax^2 +bx+cis a perfect square.

ax^2 +bx+c= 0

b^2  4 ac,

Solving a Quadratic Equation with Only One Solution

Solve

Subtract 20x; standard form

Here, and By the quadratic formula,

In this case, the discriminant is 0, and the trinomial is a

perfect square, There is just one solution, A check confirms that the

solution set is E^52 F. NOW TRY

5

12 x- 52 2.

(^2).
b^2 - 4 ac 4 x^2 - 20 x+ 25
x=

- 1 - 202  21 - 2022 - 41421252

2142

=

20  0

8

=

5

2

.

a=4,b=-20, c=25.

4 x^2 - 20 x+ 25 = 0

4 x^2 + 25 = 20 x.

NOW TRY EXAMPLE 4
EXERCISE 4
Solve 16x^2 = 8 x-1.

4. E^14 F

CAUTION Notice in the quadratic formula that the fraction bar is under as

well as the radical. Be sure to find the values of first. Then

divide those results by the value of 2 a.

b 2 b^2  4 ac

• b

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