SOLUTION: Find the imaginary solutions: x^2 + 20x + 101 = 0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find the imaginary solutions: x^2 + 20x + 101 = 0      Log On


   

Question 157994: Find the imaginary solutions: x^2 + 20x + 101 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B20x%2B101=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=20, and c=101


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-%2820%29+%2B-+sqrt%28+%2820%29%5E2-4%281%29%28101%29+%29%29%2F%282%281%29%29 Plug in a=1, b=20, and c=101


x+=+%28-20+%2B-+sqrt%28+400-4%281%29%28101%29+%29%29%2F%282%281%29%29 Square 20 to get 400.


x+=+%28-20+%2B-+sqrt%28+400-404+%29%29%2F%282%281%29%29 Multiply 4%281%29%28101%29 to get 404


x+=+%28-20+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 404 from 400 to get -4


x+=+%28-20+%2B-+sqrt%28+-4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-20+%2B-+2%2Ai%29%2F%282%29 Take the square root of -4 to get 2%2Ai.


x+=+%28-20+%2B+2%2Ai%29%2F%282%29 or x+=+%28-20+-+2%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-20%29%2F%282%29+%2B+%282%2Ai%29%2F%282%29 or x+=++%28-20%29%2F%282%29+-+%282%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+-10%2Bi or x+=++-10-i Reduce.


So the answers are x+=+-10%2Bi or x+=++-10-i