1. Equations & Inequalities

Match the equation in Column I with its solution(s) in Column II. x^2 = 25

Solve each equation in Exercises 1 - 14 by factoring. x^2 = 8x - 15

Match the equation in Column I with its solution(s) in Column II. x^2 - 5 = 0

Solve each equation in Exercises 1 - 14 by factoring. 6x^2 + 11x - 10 = 0

Solve each equation in Exercises 1 - 14 by factoring. 3x^2 - 2x = 8

Solve each equation in Exercises 1 - 14 by factoring. 3x^2 + 12x = 0

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it

Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive integers whose product is 110.

Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. Find two consecutive even integers whose product is 168.

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations does not require Step 1 of the method for completing the square described in this section. Which one is it? Solve it.

Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x - 7) = 0 Only one of the equations is set up so that the values of a, b, and c can be determined immediately. Which one is it? Solve it.

Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. The sum of the squares of two consecutive odd integers is 202. Find the integers

Solve each equation in Exercises 15–34 by the square root property. 3x^2 = 27

Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x represents an integer, then x+1 represents the next consecutive integer.If x represents an even integer, then x+2 represents the next consecutive even integer.If x represents an odd integer, then x+2 represents the next consecutive odd integer. The sum of the squares of two consecutive even integers is 52. Find the integers.

Solve each equation in Exercises 15–34 by the square root property. 5x^2 = 45

Solve each equation using the zero-factor property. See Example 1. 2x^2 - x = 15

Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10

Solve each equation in Exercises 15–34 by the square root property. 3x^2 - 1 = 47

Solve each equation in Exercises 15–34 by the square root property. 2x^2 - 5 = - 55

Solve each problem. See Examples 1 and 2. Dimensions of a Square. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares.

Solve each equation using the zero-factor property. See Example 1. 9x^2 - 12x + 4 = 0

Solve each problem. See Examples 1. Dimensions of a Parking Lot. A parking lot has a rectangular area of 40,000 yd2. The length is 200 yd more than twice the width. Find the dimensions of the lot.

Solve each equation using the zero-factor property. See Example 1. 36x^2 + 60x + 25 = 0

Solve each equation in Exercises 15–34 by the square root property. (x - 3)^2 = - 5

Solve each equation using the square root property. See Example 2. 48 - x^2 = 0

Solve each equation in Exercises 15–34 by the square root property. (3x + 2)^2 = 9

Manufacturing to Specifications. A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8π ft2. What should the radius of the circular top and bottom of the container be? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.)

Solve each equation using the square root property. See Example 2. x^2 = -400

Solve each equation in Exercises 15–34 by the square root property. (4x - 1)^2 = 16

Solve each equation in Exercises 15–34 by the square root property. (8x - 3)^2 = 5

Radius of a CanA can of Blue Runner Red Kidney Beans has surface area 371 cm^2. Its height is 12 cm. What is the radius of the circular top? Round to the nearest hun-dredth.

Solve each equation using completing the square. See Examples 3 and 4. x^2 - 7x + 12 = 0

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 + 3x

Solve each problem. See Example 2. Length of a WalkwayA nature conservancy group decides to construct a raised wooden walkway through a wetland area. To enclose the most interesting part of the wetlands, the walkway will have the shape of a right triangle with one leg 700 yd longer than the other and the hypotenuse 100 yd longer than the longer leg. Find the total length of the walkway.

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - 7x

Solve each equation using completing the square. See Examples 3 and 4. x^2 - 2x - 2 = 0

Solve each equation. -2x² +11x = -21

Solve each equation using completing the square. See Examples 3 and 4. 2x^2 + x = 10

Solve each equation. (2x+1)(x-4) = x

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - (2/3)x

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - (1/3)x

Solve each equation using completing the square. See Examples 3 and 4. -3x^2 + 6x + 5 = 0

Solve each equation. (x+4)(x+2) = 2x

Which equation has two real, distinct solutions? Do not actually solve. A. (3x-4)² = -9 B. (4-7x)² = 0 C. (5x-9)(5x-9) = 0 D. (7x+4)² = 11

Solve each equation using completing the square. See Examples 3 and 4. 3x^2 - 9x + 7 = 0

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - x - 1 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 - 6x - 11 = 0

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 16x² +3 = -26x

Solve each equation in Exercises 47–64 by completing the square. x^2 + 4x + 1 = 0

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 6x = -7

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 = 2x - 5

Solve each equation in Exercises 47–64 by completing the square. x^2 - 5x + 6 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 + 3x - 1 = 0

Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = 8

Solve each problem. Dimensions of a Right TriangleThe shortest side of a right triangle is 7 in. shorter than the middle side, while the longest side (the hypot-enuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Solve each equation using the quadratic formula. See Examples 5 and 6. 2/3x^2 + 1/4x = 3

Solve each equation using the quadratic formula. See Examples 5 and 6. (4x - 1)(x + 2) = 4x

Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 5x - 10 = 0

Solve each equation in Exercises 65–74 using the quadratic formula. x^2 + 8x + 15 = 0

Solve each equation in Exercises 65–74 using the quadratic formula. x^2 + 5x + 3 = 0

Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 - 27 = 0

Solve each equation in Exercises 65–74 using the quadratic formula. 3x^2 - 3x - 4 = 0

Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 + 64 = 0

Solve each equation in Exercises 68–70 using the quadratic formula. 2x^2 = 3-4x

In Exercises 71–72, without solving the given quadratic equation, determine the number and type of solutions. 9x^2 = 2-3x

Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. r = r_0+(1/2)at^2, for t

Solve each equation in Exercises 73–81 by the method of your choice. (x-3)^2 - 25 = 0

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. h = -16t^2+v_0t+s_0, for t

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. 2x^2 - 11x + 3 = 0

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 2x + 1 = 0

For each equation, (b) solve for y in terms of x. See Example 8. 4x^2 - 2xy + 3y^2 = 2

For each equation, (a) solve for x in terms of y. See Example 8. 2x^2 + 4xy - 3y^2 = 2

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 3x - 7 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - x = 1

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 3x^2 + 5x + 2 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 4x^2 = -6x + 3

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9. 8x^2 - 72 = 0

Solve each equation in Exercises 83–108 by the method of your choice. (2x + 3)(x + 4) = 1

Solve each equation in Exercises 83–108 by the method of your choice. (2x - 5)(x + 1) = 2

Solve each equation in Exercises 83–108 by the method of your choice. (3x - 4)^2 = 16

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) 4, 5

Solve each equation in Exercises 83–108 by the method of your choice. 3x^2 - 12x + 12 = 0

Solve by completing the square: 2x² – 5x + 1 = 0.

Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 4x + 29 = 0

Solve each equation in Exercises 83–108 by the method of your choice. x^2 = 4x - 7

Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - 7x = 0

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = x^2 - 4x - 5

In Exercises 109–114, find the x-intercept(s) of the graph of each equation. Use the x-intercepts to match the equation with its graph. The graphs are shown in [- 10, 10, 1] by [- 10, 10, 1] viewing rectangles and labeled (a) through (f). y = - (x + 1)^2 + 4

In Exercises 115–122, find all values of x satisfying the given conditions. y = 2x^2 - 3x and y = 2

In Exercises 115–122, find all values of x satisfying the given conditions. y = 5x^2 + 3x and y = 2

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = - x^2 + 4x - 2, y2 = - 3x^2 + x - 1, and y1 - y2 = 0

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Use specific values for x and y to show that, in general, 1/x + 1/y is not equivalent to 1 / x + y.