1. Equations & Inequalities

Solve each equation. -2x² +11x = -21

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

Solve the given quadratic equation using the square root property. $\left(x-\frac12\right)^2-5=0$

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

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

Match the equation in Column I with its solution(s) in Column II. x² + 5 = 0

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.

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 odd integers whose product is 63.

Solve each equation using the zero-factor property. x² + 2x - 8 = 0

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

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 the zero-factor property. x² - 64 = 0

Solve each equation in Exercises 15–34 by the square root property. $(x+3{)}^2=-16$

Volume of a Box. A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 835 in.³, what were the original dimensions of the piece of metal?

Solve each equation using the square root property. 27 - x² = 0