How do I solve the following problem? When I try to answer, I cannot factor the polynomial that I get in order to solve for x. What am I doing wrong? A rectangle has sides of x+7 and x-5. What value of x gives an area of 63?

Expert Answers

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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+7)(x-5)= 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`


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