SOLUTION: x^2-8x+17=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x^2-8x+17=0      Log On


   

Question 185939: x^2-8x+17=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-8x%2B17=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-8, and c=17


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-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2817%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-8, and c=17


x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%2817%29+%29%29%2F%282%281%29%29 Negate -8 to get 8.


x+=+%288+%2B-+sqrt%28+64-4%281%29%2817%29+%29%29%2F%282%281%29%29 Square -8 to get 64.


x+=+%288+%2B-+sqrt%28+64-68+%29%29%2F%282%281%29%29 Multiply 4%281%29%2817%29 to get 68


x+=+%288+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 68 from 64 to get -4


x+=+%288+%2B-+sqrt%28+-4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%288+%2B-+2%2Ai%29%2F%282%29 Take the square root of -4 to get 2%2Ai.


x+=+%288+%2B+2%2Ai%29%2F%282%29 or x+=+%288+-+2%2Ai%29%2F%282%29 Break up the expression.


x+=+%288%29%2F%282%29+%2B+%282%2Ai%29%2F%282%29 or x+=++%288%29%2F%282%29+-+%282%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+4%2Bi or x+=++4-i Reduce.


So the answers are x+=+4%2Bi or x+=+4-i