SOLUTION: I have tried to solve the equations many times, each time I come up with a different answer, Please help me with a step-by-step guide. (x-3)^2+(x+2)^2=17

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have tried to solve the equations many times, each time I come up with a different answer, Please help me with a step-by-step guide. (x-3)^2+(x+2)^2=17      Log On


   

Question 320015: I have tried to solve the equations many times, each time I come up with a different answer, Please help me with a step-by-step guide.
(x-3)^2+(x+2)^2=17
Found 2 solutions by Earlsdon, mananth:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
%28x-3%29%5E2%2B%28x%2B2%29%5E2+=+17 Expand the two terms in parentheses.
%28x%5E2-6x%2B9%29%2B%28x%5E2%2B4x%2B4%29+=+17 Simplify the left side.
2x%5E2-2x%2B13+=+17 Subtract 17 from both sides.
2x%5E2-2x-4+=+0 Factor 2 from the left side.
2%28x%5E2-x-2%29+=+0 Apply the zero product rule.
x%5E2-x-2+=+0 Factor the left side.
%28x-2%29%28x%2B1%29+=+0 Apply the zero product rule.
x-2+=+0 or x%2B1+=+0 so...
highlight%28x+=+2%29 or highlight%28x+=+-1%29

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(x-3)^2+(x+2)^2=17
x^2-6x+9 +x^2+4x+4=17
x^2+x^2-6x+4x+9+4=17
2x^2-2x+13=17
2x^2-2x+13-17=0
2x^2-2x-4=0
Divide by 2
x^2-x-2=0
x^2-2x+x-2=0
x(x-2)+1(x-2)=0
(x+1)(x-2)=0
x=-1 OR x=2