1. Equations & Inequalities

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.x^2 - (1/3)x

Solve each equation using completing the square. See Examples 3 and 4. -3x^2 + 6x + 5 = 0

Solve each equation. (x+4)(x+2) = 2x

Which equation has two real, distinct solutions? Do not actually solve.A. (3x-4)² = -9B. (4-7x)² = 0C. (5x-9)(5x-9) = 0D. (7x+4)² = 11

Solve each equation using completing the square. See Examples 3 and 4. 3x^2 - 9x + 7 = 0

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - x - 1 = 0

Solve each equation in Exercises 47–64 by completing the square.x^2 - 6x - 11 = 0

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

Solve each equation in Exercises 47–64 by completing the square.x^2 + 4x + 1 = 0

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 6x = -7

Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 = 2x - 5

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