4y² − 9y = 28

x² = 5(x + 100)

6x(x − 1) = 6 − 11x

x² + 8x − 2 = 0

 

x=

 

 

7. Find all real solutions of the equation by completing the square. (Enter your answers as a comma-separated list.)

x=

 

 

8.  ind all real solutions of the equation by completing the square. (Enter your answers as a comma-separated list.)

x=

 

 

9. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

x=

 

 

10. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

y=

 

11. Use the Quadratic Formula and a calculator to find all real solutions, rounded to three decimals. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)

x=

 

 

 

12.  Solve the equation for the indicated variable. (Enter your answers as a comma-separated list.) 

 

$$\begin{gathered} \frac{1}{r}+\frac{4}{1–r}=\frac{8}{r^2}; for r \\ r= \end{gathered}$$

 

 

13.  Use the discriminant to determine the number of real solutions of the equation. Do not solve the equation. 

$6x^2+4x+\frac{11}{8}=0$

 

 

14.  Find all values of k that ensure that the given equation has exactly one solution. (Enter your answers as a comma-separated list.) 

 

$4x^2+kx+81=0$

 

 

k=

 

 

15.  A rectangular garden is 6 ft longer than it is wide. Its area is 475 ft². What are its dimensions? 

width = __ft

length = __ ft

 

 

16.  A salesman drives from Ajax to Barrington, a distance of 140 mi, at a steady speed. He then increases his speed by 10 mi/h to drive the 168 mi from Barrington to Collins. If the second leg of his trip took 4 min more time than the first leg, how fast was he driving between Ajax and Barrington? 

 

___ mi/hr

 

17. Suppose an object is dropped from a height h0 above the ground. Then its height after t seconds is given by h = −16

$t^2$

+

$h_0$

,where h is measured in feet. Use this information to solve the problem.

A ball is dropped from the top of a building 89 ft tall. (Round your answers to three decimal places.)
(a) How long will it take to fall half the distance to ground level?
t = ____ sec

(b) How long will it take to fall to ground level?
t = 2.358 sec