1. Equations & Inequalities

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 difference of the squares of two positive consecutive odd integers is 32. Find the integers.

Solve each equation using the zero-factor property. See Example 1. x^2 - 64 = 0

Solve each equation in Exercises 15–34 by the square root property.(x + 3)^2 = - 16

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 832 in.^3, what were the original dimensions of the piece of metal?

Solve each equation using the square root property. See Example 2. 27 - x^2 = 0

Dimensions of a SquareWhat is the length of the side of a square if its area and perimeter are numerically equal?

Solve each equation using the square root property. See Example 2. (4x + 1)^2 = 20

Solve each equation using the square root property. See Example 2. (-2x + 5)^2 = -8

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 - 10x

Solve each equation. 2x²+x-15 = 0

Solve each equation. x²- √5x -1 = 0

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

Solve each equation in Exercises 47–64 by completing the square.x^2 + 4x = 12

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. -8x² + 10x = 7

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 3x - 2 = 0