1. Equations & Inequalities

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