1. Equations & Inequalities

Solve each equation in Exercises 1 - 14 by factoring. x^2 - 3x - 10 = 0

Match the equation in Column I with its solution(s) in Column II. x^2 + 5 = 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 square root property? 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. Find two consecutive odd integers whose product is 63.

Solve each equation using the zero-factor property. See Example 1. x^2 + 2x - 8 = 0

Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)^2

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

Solve each equation using the quadratic formula. See Examples 5 and 6. 1/2x^2 + 1/4x - 3 = 0

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

Solve each equation using the quadratic formula. See Examples 5 and 6. (3x + 2)(x - 1) = 3x

Solve each equation in Exercises 66–67 by completing the square. 3x^2 -12x+11= 0

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. F = kMv^2/r , for v

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 4x - 5 = 0

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

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. x^2 - 8x + 16 = 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. 9x^2 + 11x + 4 = 0

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

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.) i, -i

Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 6x + 13 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)

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

In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression. 3/(2x^2 + 4x - 9)

In Exercises 127–130, solve each equation by the method of your choice. √2 x^2 + 3x - 2√2 = 0

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |2x^2 - 4| = |2x^2|

Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | x2 + 1 | - | 2x | = 0

Solve each equation. See Example 7. (x^2+24)^1/4 = 3

Solve each equation. See Example 7. (x-3)^2/5 = 4