1. Equations & Inequalities

Solve each equation. 2x²+x-15 = 0

Solve each equation. x²- √(5x) -1 = 0

Solve each equation using completing the square. -2x² + 4x + 3 = 0

Solve each equation in Exercises 47–64 by completing the square. $x^2+4x=12$

Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. -8x² + 10x = 7

Solve each equation using the quadratic formula. x² - 3x - 2 = 0

Solve each equation using the quadratic formula. (1/2)x² + (1/4)x - 3 = 0

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

Solve each equation using the quadratic formula. See Examples 5 and 6.

$(3x+2)(x-1)=3x$

Solve each equation for the specified variable. (Assume no denominators are 0.) F = kMv²/r , for v

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

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) x² - 8x + 16 = 0

Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and tell whether they are rational, irrational, or nonreal complex numbers. (Do not solve the equation.) See Example 9.

$9x^2+11x+4=0$

Solve each equation in Exercises 83–108 by the method of your choice. $x^2-2x=1$

Answer each question. Find the values of a, b, and c for which the quadratic equation. ax² + bx + c = 0 has the given numbers as solutions. (Hint: Use the zero-factor property in reverse.) i, -i