Given the sides of a rectangle are : (x+7) and (x-5)
Also, given that the area of the rectangle is 63.
Then, the product of the sides of the rectangle is 63.
`==> x^2 + 2x -35 = 63`
`==> x^2 + 2x -98 = 0`
Now we will use the quadratic formula to solve for x.
`x = (-b+sqrt(b^2-4ac))/(2a)`
`==> x1= (-2+sqrt(396))/2 = (-2+6sqrt11)/2 = -1+3sqrt11`
`==> x2= -1-3sqrt11`
Now we will test our answers by finding the value of the sides.
`x1+7 = -1+3sqrt11 +7 = 6+3sqrt11 >0`
`x1-5 = -1+3sqrt11 -5 = -6+3sqrt11 >0`
`x2+7 = -1-3sqrt11 +7 = 6-3sqrt11 <0`
Then, x2 is not a valid answer because the sides can not be negative values.
`==> x = -1+3sqrt11`