SOLUTION: x^2+2x+5=0

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Question 498757: x^2+2x+5=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B2x%2B5=0 Start with the given equation.


Notice that the quadratic x%5E2%2B2x%2B5 is in the form of Ax%5E2%2BBx%2BC where A=1, B=2, and C=5


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%285%29+%29%29%2F%282%281%29%29 Plug in A=1, B=2, and C=5


x+=+%28-2+%2B-+sqrt%28+4-4%281%29%285%29+%29%29%2F%282%281%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4-20+%29%29%2F%282%281%29%29 Multiply 4%281%29%285%29 to get 20


x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 20 from 4 to get -16


x+=+%28-2+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-2+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%28-2+%2B+4%2Ai%29%2F%282%29 or x+=+%28-2+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-2%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%28-2%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+-1%2B2%2Ai or x+=++-1-2%2Ai Reduce.


So the solutions are x+=+-1%2B2%2Ai or x+=+-1-2%2Ai where i=sqrt%28-1%29