1. Equations & Inequalities

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.

$r=r_0+\left(\frac{1}{2}\right)a{t}^2$, for t

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x² - 10x

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.) 4x² = -6x + 3

Solve each equation. (x²+24x)^1/4 = 3

Use 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 odd integers is 32. Find the integers.

Solve each equation using completing the square. -2x² + 4x + 3 = 0

Solve each equation using the square root property. (4x + 1)² = 20

For each equation, (b) solve for y in terms of x. See Example 8.

$2x^2+4xy-3y^2=2$

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

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

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 83–108 by the method of your choice. $x^2-6x+13=0$

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

Use 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 odd integers is 202. Find the integers.

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 16x² +3 = -26x