SOLUTION: Hello! I'm having trouble getting the correct answer for this problem with the quadratic formula. I keep getting the answer -1+2i and -1-2i Find all solutions of the equation a

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hello! I'm having trouble getting the correct answer for this problem with the quadratic formula. I keep getting the answer -1+2i and -1-2i Find all solutions of the equation a      Log On


   

Question 196504: Hello!
I'm having trouble getting the correct answer for this problem with the quadratic formula. I keep getting the answer -1+2i and -1-2i
Find all solutions of the equation and express them in the form a + bi.
x^2+2x+2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B2x%2B2=0 Start with the given equation.


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


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


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


x+=+%28-2+%2B-+sqrt%28+4-8+%29%29%2F%282%281%29%29 Multiply 4%281%29%282%29 to get 8


x+=+%28-2+%2B-+sqrt%28+-4+%29%29%2F%282%281%29%29 Subtract 8 from 4 to get -4


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


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


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


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


x+=+-1%2Bi or x+=+-1-i Reduce.


So the answers are x+=+-1%2Bi or x+=+-1-i