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

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.x^2 - 2x + 1 = 0

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

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