SOLUTION: x^2+(x-10)^2=22^2 this is ia formula i came up with for a word problem. Im pretty confident that this is the right equation but i have no idea how to solve it.

Algebra ->  Expressions-with-variables -> SOLUTION: x^2+(x-10)^2=22^2 this is ia formula i came up with for a word problem. Im pretty confident that this is the right equation but i have no idea how to solve it.       Log On


   

Question 822830: x^2+(x-10)^2=22^2
this is ia formula i came up with for a word problem. Im pretty confident that this is the right equation but i have no idea how to solve it.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%28x-10%29%5E2=22%5E2
x%5E2+%2B+x%5E2-20x%2B100+=+484
2x%5E2+-+20x+-+384+=+0
x%5E2+-+10x+-+192+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B-192+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-10%29%5E2-4%2A1%2A-192=868.

Discriminant d=868 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+868+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+868+%29%29%2F2%5C1+=+19.7309198626562
x%5B2%5D+=+%28-%28-10%29-sqrt%28+868+%29%29%2F2%5C1+=+-9.73091986265623

Quadratic expression 1x%5E2%2B-10x%2B-192 can be factored:
1x%5E2%2B-10x%2B-192+=+%28x-19.7309198626562%29%2A%28x--9.73091986265623%29
Again, the answer is: 19.7309198626562, -9.73091986265623. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B-192+%29