A teacher is monitoring her class while the students are involved in a group activity exploring the size of angles in a set of triangles. She moves from group to group, pausing and watching the group dynamics. What the teacher is doing can best be described as:

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

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explanation:

first, the romans stayed isolated because they had to defend their own territories from neighboring cities that were harassing them, like the etruscans. second, once the romans managed to defeat their neighbors, and started to expand their territory, they started to build roads and bridges. finally, now that the romans have covered their territory with roads functioning as highways, they could mobilize their legions faster to assemble larger military units in a specific place

can you explain it better