The positive value for x is 7
Explanation:
Given that the area of a rectangle is expressed by [tex]2x^2-7x-4[/tex]
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,
[tex]2x^{2} -7x-4=45[/tex]
Subtracting both sides by 45, we have;
[tex]2x^{2} -7x-49=0[/tex]
Let us solve the equation using the quadratic formula.
Thus, we get;
[tex]x=\frac{-(-7) \pm \sqrt{(-7)^2-4(2)(-49)}}{2(2)}[/tex]
Simplifying, we get;
[tex]x=\frac{7 \pm \sqrt{49+392}}{4}[/tex]
[tex]x=\frac{7 \pm \sqrt{441}}{4}[/tex]
[tex]x=\frac{7 \pm 21}{4}[/tex]
Thus, the two values of x are given by
[tex]x=\frac{7 + 21}{4}[/tex] and [tex]x=\frac{7 - 21}{4}[/tex]
[tex]x=\frac{28}{4}[/tex] and [tex]x=\frac{-14}{4}[/tex]
[tex]x=7[/tex] and [tex]x=-\frac{7}{2}[/tex]
Since, x cannot take negative values, then [tex]x=7[/tex]
Thus, the value of x is 7.
