Exercise 14 Page 60

After the substitution, rewrite the equation so that there is a difference of two squares on the left-hand side.

60 mph

Practice makes perfect

To find the speed of the car, we need to substitute 150 for d into this formula.

1/24s^2=d

d= 150

1/24s^2= 150

LHS * 24=RHS* 24

s^2=3600

Notice that 3600 is the square of 60. Let's rewrite it so all terms are on the left-hand side and then factor it.

s^2=3600

Write as a power

s^2=60^2

LHS-60^2=RHS-60^2

s^2-60^2=0

a^2-b^2=(a+b)(a-b)

(s-60)(s+60)=0

To solve this equation, we will apply the Zero Product Property.

(s-60)(s+60)=0

Use the Zero Product Property

lcs-60=0 & (I) s+60=0 & (II)

(I): LHS+60=RHS+60

ls=60 s+60=0

(II): LHS-60=RHS-60

ls_1=60 s_2=- 60

Since speed cannot be negative, we ignore the negative solution. The speed of the car is 60 mph.

Exercises p.60-63

Hints