1. Equations & Inequalities

Find all values of x satisfying the given conditions. y₁ = x - 1, y₂ = x + 4 and y₁y₂ = 14

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $3x^4=81x$

Solve the given quadratic equation using the quadratic formula. $3x^2+4x+1=0$

Solve the given quadratic equation using the quadratic formula. $2x^2-3x=-3$

Determine the number and type of solutions of the given quadratic equation. Do not solve. 

$x^2+8x+16=0$

Determine the number and type of solutions of the given quadratic equation. Do not solve. 

$-4x^2+4x+5=0$

Solve each equation in Exercises 1 - 14 by factoring. $2x(x-3)=5x^2-7x$

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

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

Solve each equation in Exercises 15–34 by the square root property. (x + 2)² = 25

Solve each equation in Exercises 15–34 by the square root property. $3(x-4{)}^2=15$

Solve each equation in Exercises 15–34 by the square root property. $(x+3{)}^2=-16$

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

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. $x^2+12x$

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