1. Equations & Inequalities

Solve each equation using the quadratic formula. (1/2)x² + (1/4)x - 3 = 0

Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)²

Solve each cubic equation using factoring and the quadratic formula. See Example 7.

$x^3-27=0$

List all numbers that must be excluded from the domain of each rational expression. 3/(2x² + 4x - 9)

Use Choices A–D to answer each question. A. 3x² - 17x - 6 = 0 B. (2x + 5)² = 7 C. x² + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the square root property? Solve it.

Height of a Projectile A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=-16t²+v₀t. In each exercise, find the time(s) that the projectile will (a) reach a height of 80 ft and (b) return to the ground for the given value of v₀. Round answers to the nearest hundredth if necessary. v₀=96

Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

Solve each equation using the square root property. See Example 2. x² = 121

Solve each equation in Exercises 1 - 14 by factoring. $x^2-3x-10=0$

Solve the given quadratic equation using the square root property. $2x^2-16=0$

Dimensions of a Rug. Zachary wants to buy a rug for a room that is 12 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 108 ft² of carpeting. What dimensions should the rug have?

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 even integers is 52. Find the integers.

For each equation, solve for x in terms of y. 4x² - 2xy + 3y² = 2

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax² + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) i, -i

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. Find two consecutive even integers whose product is 168.