Question

Rectangle has an

Answer 1

The positive value for x is 7

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;

$x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-49)}}{2(2)}$

Simplifying, we get;

$x=\frac{7 \pm \sqrt{49+392}}{4}$

$x=\frac{7 \pm \sqrt{441}}{4}$

$x=\frac{7 \pm 21}{4}$

Thus, the two values of x are given by

$x=\frac{7 + 21}{4}$   and   $x=\frac{7 - 21}{4}$

$x=\frac{28}{4}$   and   $x=\frac{-14}{4}$

$x=7$   and   $x=-\frac{7}{2}$

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

Thus, the value of x is 7.