1. Equations & Inequalities

Solve each equation in Exercises 47–64 by completing the square.x^2 - 5x + 6 = 0

Solve each equation in Exercises 47–64 by completing the square.x^2 + 3x - 1 = 0

Solve each problem. Dimensions of a Right TriangleThe shortest side of a right triangle is 7 in. shorter than the middle side, while the longest side (the hypot-enuse) is 1 in. longer than the middle side. Find the lengths of the sides.

Solve each equation using the quadratic formula. See Examples 5 and 6. 2/3x^2 + 1/4x = 3

Solve each equation using the quadratic formula. See Examples 5 and 6. (4x - 1)(x + 2) = 4x

Solve each equation in Exercises 47–64 by completing the square.3x^2 - 5x - 10 = 0

Solve each equation in Exercises 65–74 using the quadratic formula.x^2 + 8x + 15 = 0

Solve each equation in Exercises 65–74 using the quadratic formula.x^2 + 5x + 3 = 0

Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 - 27 = 0

Solve each equation in Exercises 65–74 using the quadratic formula.3x^2 - 3x - 4 = 0

Solve each cubic equation using factoring and the quadratic formula. See Example 7. x^3 + 64 = 0

Solve each equation in Exercises 68–70 using the quadratic formula. 2x^2 = 3-4x

In Exercises 71–72, without solving the given quadratic equation, determine the number and type of solutions. 9x^2 = 2-3x

Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0

Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. r = r_0+(1/2)at^2, for t