# ALGEBRA

ALGEBRA HOMEWORK

Directions: Please show all of your work for each problem. If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word. There is a tutorial on using this equation editor in Module 1 Lecture Notes. You also have the option of hand writing your work and scanning it.

1. Solve for x. x2 + 2 = 6
X^2 = 4
X = 2, -2

2. Solve for x. (x + 4)2 = 3
X = -4 + srt(3)
X =-4 – sqrt(3)

3. Solve for x. –9(x – 3)2 = –7
(x-3)^2 = 7/9
X = 3 + sqrt(7/9), 3 – sqrt(7/9)

4. The base of a 19-ft ladder is 6 feet away from the wall. How far above the floor is the top of the ladder? Give your answer to the nearest thousandth.
X = sqrt(19^2 – 6^2) = 18.03

5. Solve the equation for x. (2x – 1)2 – 9 = 0
(2x-1)^2 = 9
X=-1, 2

6. The square of 3 more than a number is 36. Find the number.
(x+3)^2=36
X=-9, 3

7. Determine whether the following trinomial is a perfect square.x2 + 4x + 4
(x+2)^2, yes perfect square

8. Find the constant term that should be added to make the following expression a perfect-square trinomial.x2 + 7x
(7/2)^2 = 49/4

9. Solve by completing the square. x2 – 4x – 60 = 0
X^2-4x + 4 = 60+4 = 64
(x-2)^2 = 64
X=10, -6

10. The length of a rectangle is 5 cm more than 4 times its width. If the area of the rectangle is 60 cm2, find the dimensions of the rectangle to the nearest thousandth.
X(4x+5) = 60
X=3.298
length=18.192
11. Find two consecutive positive integers such that the sum of their squares is 61.
X^2 + (x+1)^2 = 61
X=5
5 and 6

12. Use the quadratic formula to solve the following equation. x2 = –x + 7
X=(-1+sqrt(29))/2, (-1-sqrt(29))/2

13. Use the quadratic formula to solve the following equation. 2×2 + 3x – 3 = 0
X=(-3-sqrt(33)/4, (-3+sqrt(33))/4

14. The height h in feet of an object after t seconds is given by the function:
h = –16t2 + 40t + 8. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

15. Solve for x.

16. Solve. (x – 3)2 = 6Solve a quadratic equation by completing the square
X = 3+sqrt(6), 3-sqrt(6)

17. Solve. 2×2 – 5x – 10 = 0Solve a quadratic question using the quadratic formula
X=(5-sqrt(105))/4, (5+sqrt(105))/4
18. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2+16x
(16/2)^2 = 64

19. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2-12x
(12/2)^2 = 36

20. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2+2x
(2/2)^2 = 1

21. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2-8x
(8/2)^2 = 16

22. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2+x
(1/2)^2 = ¼

23. Find the constant term that should be added to make the following expression a perfect-square trinomial.X^2+9x
(9/2)^2 = 81/4

24. Solve by completing the square.X^2+8x=-15
X=-5, -3

25. Solve by completing the square.X^2+6x+2=0
X=-3-sqrt(7), -3+sqrt(7)

26. Solve by completing the square.X^2+x-1=0
X=(-1+sqrt(5))/2, (-1-sqrt(5))/2

27. Solve by using the quadratic formula.X^2+11x-12=0
X=-12, 1

28. Solve by using the quadratic formula.X^2-6x+9=0
(x-3)^2 = 0
X=3

29. Solve by using the quadratic formula.3x^2-7x=3
X = (7+sqrt(85))/6, (7-sqrt(85))/6

30. An entry in the Apple Festival Poster Contest must be rectangular and have an area of 1200 square inches. Also, its length must be 20 inches longer than its width. Find the dimensions each entry must have.
X(x+20)=1200
X^2 + 20x – 1200 = 0
X=26.06
Length = 46.06

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