The area of a rectangle can be expressed by 2x ^ 2 - 7x - 4 if the rectangle has an area of 45 find the positive value for x

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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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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