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

In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

Write each power of i as i, - 1, - i, or 1.

i⁴⁴

Solve each equation in Exercises 47–64 by completing the square. $x^2+3x-1=0$

In Exercises 51–58, solve each compound inequality. - 3 ≤ (2/3)x - 5 < - 1

Write each power of i as i, - 1, - i, or 1.

i¹¹⁴

Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = 8

In Exercises 59–94, solve each absolute value inequality. |x| < 3

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

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

Write each power of i as i, - 1, - i, or 1. i¹³⁵

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x| = 8

In Exercises 61–64, write each complex number in standard form. (1 + i)³

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

Solve each equation by the square root property. $\frac{x^2}{2}+5=-3$

In Exercises 59–94, solve each absolute value inequality. |x - 1| ≤ 2

Find all values of x satisfying the given conditions. y₁ = 5(2x - 8) - 2, y₂ = 5(x - 3) + 3, and y₁ = y₂.

In Exercises 59–94, solve each absolute value inequality. |x + 3| ≤ 4

Write each complex number in standard form. (1 - i)³

In Exercises 59–94, solve each absolute value inequality. |2x - 6| < 8

In Exercises 61–66, find all values of x satisfying the given conditions. $y_1 = \frac{x - 3}{5}, \quad y_2 = \frac{x - 5}{4}, \quad \text{and} \quad y_1 - y_2 = 1$

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

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

Write each complex number in standard form. (2 + 3i)³

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^2+20x$

In Exercises 59–94, solve each absolute value inequality. |3x + 5| < 17

Solve each equation in Exercises 47–64 by completing the square. 3x² - 5x - 10 = 0

Perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i) - (3 - i)(3 + i)

In Exercises 59–94, solve each absolute value inequality. |2(x - 1) + 4| ≤ 8