1. Equations & Inequalities

Solve each equation in Exercises 15–34 by the square root property. (2x + 8)² = 27

Solve each equation in Exercises 47–64 by completing the square. $x^2+6x=7$

Solve each equation in Exercises 47–64 by completing the square. $2x^2-7x+3=0$

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

Solve each equation in Exercises 83–108 by the method of your choice. $5x^2+2=11x$

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x² - 20)/(x² - 7x + 12)

Find all values of x satisfying the given conditions. y₁ = 2x² + 5x - 4, y₂ = - x² + 15x - 10, and y₁ - y₂ = 0

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Solve each equation in Exercises 41–60 by making an appropriate substitution. ${(y-\frac{8}{y})}^2+5(y-\frac{8}{y})-14=0$

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)² - 4(x - 5) - 21 = 0

Solve each equation in Exercises 41–60 by making an appropriate substitution. $x^{\frac{2}{5}}+x^{\frac{1}{5}}-6=0$

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. $(x^2-x-4{)}^{\frac{3}{4}}-2=6$