Intermediate Algebra (11th edition)

The following steps justify the square root property.

Subtract k.

Factor.

or Zero-factor property

x 2 k or x 2 k Solve each equation.

x- 2 k= 0 x+ 2 k= 0

Ax- 2 kBAx+ 2 kB = 0

x^2 - k= 0

x^2 = k

SECTION 9.1 The Square Root Property and Completing the Square 497

CAUTION If then using the square root property always produces two

square roots, one positive and one negative.

kZ 0,

Using the Square Root Property

Solve each equation.

(a)

By the square root property, if , then

or.

The solution set is E 25 , - 25 F.

x= 25 x= - 25

x^2 = 5

x^2 = 5

EXAMPLE 2

Don’t forget the

negative solution.

(b)

Add 48.

Divide by 4.

or Square root property

or

The solutions are and Check each in the original equation.

CHECK Original equation

Let Let

✓ True ✓ True

The solution set is E 223 , - 223 F. NOW TRY

0 = 0 0 = 0

48 - 48  0 48 - 48  0

41122 - 48  0 41122 - 48  0

4 A- 223 B x=- 223.

2

4 A 223 B x= 223. - 48  0

2

- 48  0

4 x^2 - 48 = 0

223 - 223.

x= 223 x= - 223 212 = 24 # 23 = 223

x= 212 x= - 212

x^2 = 12

4 x^2 = 48

4 x^2 - 48 = 0

= 22 #A 23 B^2

A 223 B^2

NOTEUsing the symbol (read “positive or negative,” or “plus or minus”), the

solutions in Example 2could be written and

Using the Square Root Property in an Application

Galileo Galilei developed a formula for freely falling objects described by

where dis the distance in feet that an object falls (disregarding air resistance) in tsec-

onds, regardless of weight. Galileo dropped objects from the Leaning Tower of Pisa.

d= 16 t^2 ,

EXAMPLE 3

 25  223.



NOW TRY

EXERCISE 2

Solve each equation.

(a)

(b) 2 x^2 - 90 = 0

t^2 = 10

NOW TRY ANSWERS

2. (a)

(b) E 325 , - 325 F

E 210 , - 210 F