Answer:
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 = - [tex]\frac{7}{2}[/tex]
Thus the positive value for x is x = 7
The positive value of x for the rectangle is 7 units.
A rectangle is a quadrilateral (has four angles and four sides) in which opposite sides are equal to each other.
Given that the area of a rectangle has an expression 2x² - 7x - 4 and has an area of 45. hence:
2x² - 7x - 4 = 45
2x² - 7x - 49 = 0
x = -3.5 and x = 7
Therefore the positive value of x for the rectangle is 7 units.
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