Monarchies were the most common form of early government. What is a monarchy? How do monarchs get their power?

Monarchy, political system based upon the undivided sovereignty or rule of a single person. The term applies to states in which supreme authority is vested in the monarch, an individual ruler who functions as the head of state and who achieves his or her position through heredity.

Explanation:

x = 7

step-by-step explanation:

equating the expression for area to the given area

2x² - 7x - 4 = 45 ( subtract 45 from both sides )

2x² - 7x - 49 = 0 ← in standard form

to factor consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 49 = - 98 and sum = - 7

the factors are - 14 and + 7

use these factors to split the middle term

2x² - 14x + 7x - 49 = 0 ( factor the first/second and third/fourth terms )

2x(x - 7) + 7(x - 7) = 0 ← factor out (x - 7)

(x - 7)(2x + 7) = 0

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

2x + 7 = 0 ⇒ 2x = - 7 ⇒ x = -

thus the positive value for x is x = 7