SOLUTION: I have a square field with an area x + 12 by x + 12. A section of it has been removed, and that area is x + 1 by x + 7. The area of the square minus the missing section is 217. T

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I have a square field with an area x + 12 by x + 12. A section of it has been removed, and that area is x + 1 by x + 7. The area of the square minus the missing section is 217. T      Log On


   

Question 67738: I have a square field with an area x + 12 by x + 12. A section of it has been removed, and that area is x + 1 by x + 7. The area of the square minus the missing section is 217.
The equation is (x + 12)^2 - (x + 1)(x + 7) = 217.
I tried using the distributive property to get x^2 + 24x + 144 - x^2 + 8x + 7 = 217.
Then I get stuck. If I combine x^2 and -x^2, I no longer have a quadratic equation, (which is the section we're studying).
What should I do? Thanks for your help.
GJL
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If the problem is to solve for x, which this appears to be, then you are proceeding correctly, except for the results of applying the distributive property. I shouldn't be too concerned with not having a quadratic equation in the final stages. Solve for x.
%28x%2B12%29%28x%2B12%29-%28x%2B1%29%28x%2B7%29+=+217
%28x%5E2%2B24x%2B144%29+-+%28x%5E2%2B8x%2B7%29+=+217 Simplify the left side.
x%5E2-x%5E2%2B24x-8x%2B144-7+=+217 Continue simplifying.
16x%2B137+=+217 Subtract 137 from both sides.
16x+=+80 Finally, divide both sides by 16.
x+=+5
As you can see, the x%5E2's drop out so you no longer have a quadratic equation but you can still solve for x.