1. Equations & Inequalities

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

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 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.

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

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

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

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

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

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

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

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

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

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

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. 9 - 6x + x^2 = 0

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. 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^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0

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

Solve each equation in Exercises 41–60 by making an appropriate substitution. (y - 8/y)^2 + 5(y - 8/y) - 14 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)^2 - 4(x - 5) - 21 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. x^(2/5) + x^(1/5) - 6 = 0

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x^2 - x - 4)^(3/4) - 2 = 6

Solve each equation in Exercises 41–60 by making an appropriate substitution. x^(-2) - x^(-1) - 6 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. x - 13√x + 40 = 0

Solve each equation in Exercises 96–102 by the method of your choice. 2√(x-1) = x

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 19) - 8 = x

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1

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

Solve each radical equation in Exercises 88–89. √ (2x-3) + x = 3

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.) | x^2 + 5x + 5 | = 1

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.) | x^2 - 9 | = x + 3

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.) | 4x^2 - 23x - 6 | = 0

Match each equation in Column I with the correct first step for solving it in Column II. (x+5)^2/3 - (x+5)^1/3 - 6 = 0

Solve each equation. See Examples 4–6. x - √(2x+3) = 0

Solve each equation. See Examples 4–6. √(3x+7) = 3x+5

Solve each equation. See Examples 4–6. √(4x+13) = 2x-1

Solve each equation. √x+2-x = 2

Solve each equation. See Examples 4–6. √(6x+7) - 9 = x-7

Solve each equation. See Examples 4–6. √2x-x+4=0

Solve each equation. See Examples 4–6. √4x-x+3=0

Solve each equation. See Examples 4–6. √(2x+5)-√(x+2)=1

Solve each equation. See Examples 4–6. √(4x+1)-√(x-1)=2

Solve each equation. See Examples 4–6. √3x=√(5x+1)-1

Solve each equation. See Examples 4–6. √2x=√(3x+12)-2

Solve each equation. See Examples 4–6. √(x+2)=1-√(3x+7)

Solve each equation. See Examples 4–6. √(2x-5)=2+√(x-2)

Solve each equation. See Examples 4–6. √(2√(7x+2)) = √(3x+2)

Solve each equation. See Examples 4–6. √(3√(2x+3)) = √(5x-6)

Solve each equation. See Examples 4–6. 3-√x=√(2√(x)-3)

Solve each equation. See Examples 4–6. √x+2=√(4+7√x)

Solve each equation. See Examples 4–6. ∜(x^2+2x)= ∜3

Solve each equation. (x-2)^2/3 = x^1/3

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

Solve each equation. See Example 7.(x-3)^2/5=(4x)^1/5

Solve each equation. See Example 7. x^2/3 = 2x^1/3

Solve each equation. See Example 7. 3x^3/4 = x^1/2

Solve each equation. See Examples 8 and 9. 2x^4-7x^2+5=0

Solve each equation. (2x+3)^2/3 + (2x+3)^1/3 - 6 = 0

Solve each equation. See Examples 8 and 9. (x-1)^2/3+(x-1)^1/3 -12 = 0

Solve each equation. See Examples 8 and 9. (2x-1)^2/3+2(2x-1)^1/3-3=0

Solve each equation. See Examples 8 and 9. (x+5)^2/3+(x+5)^1/3-20=0

Solve each equation. See Examples 8 and 9. 6(x+2)^4-11(x+2)^2=-4

Solve each equation. See Examples 8 and 9. 8(x-4)^4-10(x-4)^2=-3

Solve each equation. See Examples 8 and 9. 4(x+1)^4-13(x+1)^2=-9

Solve each equation. See Examples 8 and 9. 2x^-2/5-x^-1/5-1=0

Solve each equation. See Examples 8 and 9. x^-2/3+x^-1/3-6=0

Solve each equation. 2 - 5/x = 3/x²