1. Equations & Inequalities

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

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

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.

Solve each equation in Exercises 1 - 14 by factoring. 2x(x - 3) = 5x^2 - 7x

Solve each equation using the zero-factor property. See Example 1. x^2 - 5x + 6 = 0

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

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 sum of the squares of two consecutive even integers is 52. Find the integers.

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 even integers is 84. Find the integers.

Solve each equation in Exercises 15–34 by the square root property. (x + 2)^2 = 25

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 in Exercises 15–34 by the square root property. 3(x - 4)^2 = 15

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

Solve each equation using the square root property. See Example 2. x^2 = 121

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

Solve each equation using the square root property. See Example 2. (x - 4)^2 = -5

Solve each equation in Exercises 15–34 by the square root property. (2x + 8)^2 = 27

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 + 12x

Solve each equation. -2x² +11x = -21

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

(Modeling)Solve each problem. See Example 3.Height of a ProjectileA projectile is launched from ground level with an initial velocity of v_0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t^2+v_0t. In each exercise, find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v_0. Round answers to the nearest hun-dredth if necessary. v_0=96

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

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

Solve each equation in Exercises 47–64 by completing the square. x^2 + 6x = 7

See Exercise 47. (b)Which equation has two nonreal complex solutions?

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

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 8x² = -2x -6

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

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

Solve each equation using the quadratic formula. See Examples 5 and 6. -4x^2 = -12x + 11

Solve each equation in Exercises 47–64 by completing the square. 2x^2 - 7x + 3 = 0

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

Solve each equation in Exercises 60–63 by the square root property. x^2/2 + 5 = -3

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

In Exercises 64–65, 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+ 20x

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. s = (1/2)gt^2, for t

Solve each equation in Exercises 65–74 using the quadratic formula. 4x^2 = 2x + 7

Solve each equation in Exercises 65–74 using the quadratic formula. x^2 - 6x + 10 = 0

Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)

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

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

For each equation, (b) solve for y in terms of x. See Example 8. 2x^2 + 4xy - 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. 3x^2 + 5x + 2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 5x^2 + 2 = 11x

Solve each equation in Exercises 83–108 by the method of your choice. 3x^2 = 60

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

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.) -3, 2

Solve each equation in Exercises 83–108 by the method of your choice. 9 - 6x + x^2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 4x^2 - 16 = 0

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

Exercises 100–102 will help you prepare for the material covered in the next section. Factor: x^2 - 6x + 9

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

Solve each equation in Exercises 83–108 by the method of your choice. 2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)

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 = x - 1, y2 = x + 4 and y1y2 = 14

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 127–130, solve each equation by the method of your choice. 1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2 - 4)

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

Solve: √(6x - 2) = √(2x + 3) - √(4x - 1).

If a number is decreased by 3, the principal square root of this difference is 5 less than the number. Find the number(s).

If 5 times a number is decreased by 4, the principal square root of this difference is 2 less than the number. Find the number(s).

In Exercises 101–106, solve each equation. x(x + 1)^3 - 42(x + 1)^2 = 0

In Exercises 101–106, solve each equation. |x^2 + 2x - 36| = 12

In Exercises 91–100, find all values of x satisfying the given conditions. y1 = 6(2x/(x - 3))^2, y2 = 5(2x/(x - 3)), and y1 exceeds y2 by 6

In Exercises 91–100, find all values of x satisfying the given conditions. y = x - √(x - 2) and y = 4

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. |x^2 - 6| = |5x|

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 3) + √(x - 2) = 2

Solve each equation in Exercises 41–60 by making an appropriate substitution. 9x^4 = 25x^2 - 16

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 3x^4 = 81x

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.) | 3x^2 - 14x | = 5

Solve each equation. 4x⁴+3x²-1 = 0