Question

Rectangle has an

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

Answer 1

The positive value for x is 7

Step-by-step explanation:

Given that the area of a rectangle is expressed by
`2x^2-7x-4`

The area of the rectangle is 45.

We need to determine the positive value for x.

The value for x:

The value of x can be determined by equating both the values of area of a rectangle.

Thus, we have,

`2x^(2) -7x-4=45`

Subtracting both sides by 45, we have;

`2x^(2) -7x-49=0`

Let us solve the equation using the quadratic formula.

Thus, we get;

`x=(-(-7) \pm √((-7)^2-4(2)(-49)))/(2(2))`

Simplifying, we get;

`x=(7 \pm √(49+392))/(4)`

`x=(7 \pm √(441))/(4)`

`x=(7 \pm 21)/(4)`

Thus, the two values of x are given by

`x=(7 + 21)/(4)` and
`x=(7 - 21)/(4)`

`x=(28)/(4)` and
`x=(-14)/(4)`

`x=7` and
`x=-(7)/(2)`

Since, x cannot take negative values, then
`x=7`

Thus, the value of x is 7.