# Mathematics - Algebra - Quadratic Equations

Solving Quadratic Equations -

2. Give exact and approximate solutions to three decimal places.

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

3. Give exact and approximate solutions to three decimal places.

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

4. Solve by completing the square

(Use a comma to separate answers. Type exact answers, using radicals as needed. Type N if there is no solution.)

5. Solve by completing the square.

(Use a comma to separate answers. Type N if there is no solution)

6. Solve

Find the x-intercepts of

(Type a simplified fraction. Type exact answers, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

7. Solve for x

(Simplify your answers. Use a comma to separate answers. Type exact answers, using radicals as needed. Type N if there is no solution.)

8. a) Solve

b) Find the x-intercepts of

(Simplify your answer. Type exact answers, using radicals as needed. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

9. Solve for x.

(Use a comma to separate answers. Type N if there is no solution.)

10. The flower garden has the shape of a right triangle. 20ft of a perennial border forms the hypotenuse of the triangle, and one leg is 4 ft longer than other leg. Find the lengths of the legs.

(Use a comma to separate answers as needed.)

11. Solve for the indicated letter.

, for B

12. Determine the nature of the solutions of the equation.

(two non-real solutions, one real solution, two real solutions)

13. Determine the nature of the solutions of the equation.

(two non-real solutions, one real solution, two real solutions)

14. Write a quadratic equation having the given numbers as solutions.

-6 and -2

15. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,

Solution: 3, only solution

16. Solve.

(Type an exact answer, using radicals as needed. Use commas to separate answers as needed.)

17. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,

(Type an expression using x as the variable. Type an exact answer, using radicals as needed.)

18. Solve the formula for the given letter. Assume all variables represent nonnegative numbers.

, for a

19. During the first part of a trip, a canoeist travels 34 miles at a certain speed. The canoeist travels 11 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?

(Simplify your answer. Type an integer on a decimal. Round to the nearest hundredth.)

20. Solve

21. Solve

(Use a comma to separate answers as needed. Type N if the solution is not a real number.)

22. Give exact and approximate solutions to three decimal places.

(Use radicals as needed. Use a comma to separate answers.)

23.

(Use a comma to separate answers. Type N if there is no solution.)

24. Solve for r.

(Use a comma to separate answers. Type N if there is no solution.)

25. If a pro basketball player has a vertical leap of about 35 inches, what is his hang time? Use the hang-time function

(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth.)

26. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form,

Solution: 9, only solution

[See attached file for equations.]

#### Solution Preview

The solution file is attached.

1. a) Solve x = {-Ö5, Ö5}

b) Find the x-intercepts of (-Ö5, 0), (Ö5, 0)

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

2. Give exact and approximate solutions to three decimal places.

Exact solutions: x = {1, 17}; No Approximate solutions

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

3. Give exact and approximate solutions to three decimal places.

Exact solutions: x = {1, 7}; No Approximate solutions

(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)

4. Solve by completing the square

x = {3 - Ö19, 3 + Ö19}

(Use a comma to separate answers. Type exact answers, using radicals as needed. Type N if there is no solution.)

5. Solve by completing the square.

x = {-10, 6}

(Use a comma to separate answers. Type N if there is no solution)

6. Solve x = {(-7 - Ö57)/2, (-7 + Ö57)/2}

7. Find ...

#### Solution Summary

Complete, Neat and Step-by-step Solutions to all the problems are provided in the attached file.