1. Equations & Inequalities

Solve the given quadratic equation by completing the square. $x^2+3x-5=0$

Solve the given quadratic equation by completing the square.

$3x^2-6x-9=0$

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

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

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x² - 10x

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. $x^2-2x=1$

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 = 2x/(x + 2), y₂ = 3/(x + 4), and y₁ + y₂ = 1

List all numbers that must be excluded from the domain of each rational expression. 3/(2x² + 4x - 9)

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