SOLUTION: x^2 + 2x + 2 = 0 I am homeschooled, and I've been working a long time on this question, and my mom finally gave me the answer, but I can't seem to get the steps right. The

Algebra ->  Equations -> SOLUTION: x^2 + 2x + 2 = 0 I am homeschooled, and I've been working a long time on this question, and my mom finally gave me the answer, but I can't seem to get the steps right. The       Log On


   

Question 422027: x^2 + 2x + 2 = 0
I am homeschooled, and I've been working a long time on this question, and my mom finally gave me the answer, but I can't seem to get the steps right.

The answer is x = -1 + i; x = -1 - 1.
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 that the quadratic x%5E2%2B2x%2B2 is 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 solutions are x+=+-1%2Bi or x+=+-1-i

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