Asst 11

course Mth 158

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

3. The solution set of the equation (x-3)(3x+5)=0 is {3, -5/3} 5. To complete the square of the expression x^2+5x, you would add the number 5/2^2. 8. T or F - If the discriminant of a quadratic equation is positive, then the equation has two solutions that are negatives of one another. This is true. Solve by factoring -- 11. x^2-25=0 x^2 - 25 = 0 Solution set is (x+5)(x-5) = 0 {-5, 5} x+5 = 0 x-5 = 0 -5 -5 +5 +5 ___________________ x = -5 x = 5 14. ?? 17. 3t^2 - 48 = 0 3(t^2-16)=0 3(t+4)(t-4) = 0 t = 4, -4 Solution set is {4, -4} 20. x(x+4) = 12 x+4x = 12 -4 = -4 x = 8

Also x = 0

23. 6(p^2 - 1) = 5p 6p^2 - 6 = 5p 6p^2 - 5p - 6 = 0 (3p + 2)(2p - 3) = 0 p = -2/3 p = 3/2 {-2/3, 3/2} 26. x + 12/x = 7 x + 12/x = 7 x + 12 = 7 + 12 ??

If you multiply both sides of x + 12/x = 7 by x you get x^2 + 12 = 7 x. This is a quadratic equation. Rearrange to standard for x^2 - 7 x + 12 = 0, and you can easily solve by factoring.

Solve by the square root method.

29. x^2 = 25 {-5, 5} 32. (x-1)^2 = 4 2x-1 = 4 {2, -2}

You get (x-1) = +-2 .
If x-1 = 2 then x = 3. If x-1 = -2 then x = -3.

What number should be added to complete the square of each expression? 36. x^2 - 4x -4/2 = -2^2 = 4 the answer is 4 38. x^2 - 1/3 x -1/3 divided by 2/1 = -1/3 times 1/2 = -1/6 = 1/36 Solve by completing the square 41. x^2 + 4x = 21 x^2 + 4x + 4 = 21 + 4 (x-2)^2 = 25 x + 2 = the square root of 25 x + 2 = 5 x = -2 + 5 = x = 3, x = -7 {-7, 3}

x + 2 = 5 gives you x = 3 x + 2 = -5 gives you x = -7. Be sure to show these details.

44. ??? Use the quadratic formula to find real solutions if any. 47. x^2 - 4x + 2 = 0 (x+2)(x-2) = 0 x + 2 = 0 x - 2 = 0 - 2 -2 +2 +2 x = -2 x = 2 {-2, 2} 50. x^2 + 6x + 1 = 0 (x-3)(x+3) = 0 x - 3 = 0 x - 3 = 0 +3 +3 +3 +3 x = -3 x = 3 {-3, 3}

You used factoring on this problem and the last. You need to use the quadratic formula.

52. ?? 55. 4x^2 = 1 - 2x 4x^2 + 2x - 1 = 0 ????? 58. ?? 61. 3/4x^2 - 1/4x - 1/2 = 0 4(3/4x^2 - 1/4x - 1/2) = (0, 4) 3x^2 - x - 2 = 0

Good so far. Use the quadratic formula.

64. 4 + 1/x - 1/x = 0 4 + 1/x = 0 Find real solutions if any - use quadratic formula and calculator - express solutions rounded to 2 decimal places. 67. x^2 - 4.lx + 2.2 = 0 x = (-4.1) + inside square root is -4.1^2 - 4.(1)(2.2)/2(1) ___________________________ 2(1) = 4.1 + (inside square root 16.81 - 8.8 / 2 = 4.1 + inside square root 8.01 with both being divided by 2

The form in which you should express this calculation in 'typewriter notation' is
[ -(-4.1) +- sqrt( (-4.1)^2 - 4 * 1 * 2.2 ) ] / (2 * 1) = [4.1 +- sqrt(16.81 - 8.8) ] / 2 = [4.1 +- sqrt(8.01)] / 2.
You can then go on to calculate the two numbers
[4.1 + sqrt(8.01)] / 2 and [4.1 - sqrt(8.01)] / 2,
both to an appropriate number of significant figures.

70. ?? 72. Pix^2 + Pix - 2 = 0 2Pix^2 - 2 = 0

pi x^2 and pi x are not like terms, one being an x term and the other an x^2 term.
Use the quadratic formula.

75. x^2 - 5 = 0 x^2 = 5 x = +then the square root of 5 -- the solutions is (-square root of 5, and square root of 5) 78. ?? 81. 2 + z = 6z^2 6z^2 - z - 2 (3z-2)(2z+1) 3z - 2 = 0 or 2z + 1 = 0 z = 2/3 or z = 1/2 84. ?? 87. 2x^2 - 6x + 7 = 0 a = 2 b = -6 c = 7 b^2 - 4ac = (-6)^2 - 4(2)(7) = 36 - 56 = -20 no real solution 90. 25x^2 - 20x + 4 = 0 a = 25 b = -20 c = 4 b^2 - 4ac = (-20)^2 - 4(25)(4) = 400 - 116 = 284 93. Dimensions of a window- The area of the opening of a rectangular window is to be 143 sq. ft. If the length is to be 2 ft. more than the width, what are the dimensions? w(w+2) = 143 w^2 + 2w - 143 = 0 (w + 13)(w - 11) = 0 w = -13 w = 11 width is 11 and length is 13 96. ?? 98. ?? 97. An open box is to be constructed from a sq. piece of sheet metal by removing a square of side 1 foot from each corner and turning up the edges. If the box is to hold 4 cubic feet, what should the dimensions of the sheet metal be? (x-2)(x-2)(1) = 4 x^2 - 4x + 4 = 4 x^2 - 4x = 0 x(x-4) = 0 x = 0 or x = 4 100.?? "