1. Equations & Inequalities

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

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

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.x^2 - 3x - 7 = 0

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

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

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. 4x^2 = -6x + 3

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. 8x^2 - 72 = 0

Solve each equation in Exercises 83–108 by the method of your choice.(2x + 3)(x + 4) = 1

Solve each equation in Exercises 83–108 by the method of your choice.(2x - 5)(x + 1) = 2

Solve each equation in Exercises 83–108 by the method of your choice.(3x - 4)^2 = 16

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.3x^2 - 12x + 12 = 0

Solve by completing the square: 2x² – 5x + 1 = 0.

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

Solve each equation in Exercises 83–108 by the method of your choice.x^2 = 4x - 7