Answer:
Explanation:
a) Consider the quadratic equation x^2-7x-18=0.
Then we have (x-9)(x+2)=0 by factoring.
Observe that x-9=0 and x+2=0.
This implies that x=0+9=9 and x=0-2=-2.
Thus x=9, -2.
Therefore, x^2-7x-18=0.
b) Note that the area of the rectangle is determined by the equation: A=L*W where L=length and W=width.
Then we have A=x(x-7)=x^2-7x.
Observe that the area of the rectangle is 18 cm^2.
This implies that 18=x^2-7x.
Thus x^2-7x-18=0.
From our answer in part (a), we can see that the values of x are 9 and -2.
But then our length and width cannot be a negative number, so we exclude the value of x, which is -2.
Therefore, the value of x is 9.