BackUse 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.
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.
Dimensions of a Square What is the length of the side of a square if its area and perimeter are numerically equal?
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.) x2 - 8x + 16 = 0
Solve each equation. x²- √(5x) -1 = 0
Solve each equation using the quadratic formula. x2 - 3x - 2 = 0
Solve each equation. (2x+1)(x-4) = x
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 quadratic formula. x2 - 6x = -7
Use Choices A–D to answer each question. A. 3x2 - 17x - 6 = 0 B. (2x + 5)2 = 7 C. x2 + 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.
Volume of a Box. A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 835 in.3, what were the original dimensions of the piece of metal?
Solve each equation using the square root property. 48 - x2 = 0
Solve each equation in Exercises 47–64 by completing the square.
Use 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 difference of the squares of two positive consecutive even integers is 84. Find the integers.
Solve each equation using completing the square. x2 - 2x - 2 = 0