1. Equations & Inequalities

Solve each equation using the zero-factor property. 36x² + 60x + 25 = 0

Answer each question. Find the values of a, b, and c for which the quadratic equation. $a{x}^2+bx+c=0$ has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.)

$-3,2$

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. Find two consecutive odd integers whose product is 143.

Solve each equation using the zero-factor property. 9x² - 12x + 4 = 0

Solve each equation using completing the square. 2x² + x = 10

Solve each equation. (x-3)^2/5 = 4

Solve each equation by the method of your choice. √2 x² + 3x - 2√2 = 0

Use the method described in Exercises 83–86, if applicable, and properties of absolute value to solve each equation or inequality. (Hint: Exercises 99 and 100 can be solved by inspection.) | x² + 1 | - | 2x | = 0

Solve each equation using the quadratic formula. See Examples 5 and 6.

$(4x-1)(x+2)=4x$

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

Solve each equation using the quadratic formula. x² - x - 1 = 0

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. $x^2-4x-5=0$

Answer each question. Sides of a Right TriangleTo solve for the lengths of the right triangle sides, which equation is correct?

A. x^2=(2x-2)^2+(x+4)^2 B. x^2+(x+4)^2=(2x-2)^2 C. x^2=(2x-2)^2-(x+4)^2 D. x^2+(2x-2)^2=(x+4)^2

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. $\mid 2x^2-4\mid =\mid 2x^2\mid$

Solve each equation using the quadratic formula. See Examples 5 and 6.

$(3x+2)(x-1)=3x$