SOLUTION: (x-3)^2+(x+2)^2=17

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Question 174352: (x-3)^2+(x+2)^2=17
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%5E2%2B%28x%2B2%29%5E2=17 Start with the given equation.


x%5E2-6x%2B9%2Bx%5E2%2B4x%2B4=17 FOIL


x%5E2-6x%2B9%2Bx%5E2%2B4x%2B4-17=0 Subtract 17 from both sides.


2x%5E2-2x-4=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-2, and c=-4


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-2, and c=-4


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Negate -2 to get 2.


x+=+%282+%2B-+sqrt%28+4-4%282%29%28-4%29+%29%29%2F%282%282%29%29 Square -2 to get 4.


x+=+%282+%2B-+sqrt%28+4--32+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-4%29 to get -32


x+=+%282+%2B-+sqrt%28+4%2B32+%29%29%2F%282%282%29%29 Rewrite sqrt%284--32%29 as sqrt%284%2B32%29


x+=+%282+%2B-+sqrt%28+36+%29%29%2F%282%282%29%29 Add 4 to 32 to get 36


x+=+%282+%2B-+sqrt%28+36+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%282+%2B-+6%29%2F%284%29 Take the square root of 36 to get 6.


x+=+%282+%2B+6%29%2F%284%29 or x+=+%282+-+6%29%2F%284%29 Break up the expression.


x+=+%288%29%2F%284%29 or x+=++%28-4%29%2F%284%29 Combine like terms.


x+=+2 or x+=+-1 Simplify.


So the answers are x+=+2 or x+=+-1