SOLUTION: X^2+4x+8=0 Can you find the solutions and then express them in the form a+bi?

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Question 1056414: X^2+4x+8=0
Can you find the solutions and then express them in the form a+bi?
Found 3 solutions by Fombitz, ikleyn, josmiceli:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square,
x%5E2%2B4x%2B8=0
%28x%5E2%2B4x%2B4%29%2B8=4
%28x%2B2%29%5E2=-4
x%2B2=0+%2B-+sqrt%28-4%29
x%2B2=0+%2B-+2i
x=-2+%2B-+2i

Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
X^2+4x+8=0
Can you find the solutions and then express them in the form a+bi?
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Simply apply the quadratic formula:


x%5B1%2C2%5D = %28-4+%2B-+sqrt%284%5E2+-+4%2A1%2A8%29%29%2F2 = %28-4+%2B-+sqrt%28-16%29%29%2F2 = %28-4+%2B-+4i%29%2F2 = -2 +/- 2i.


x%5B1%5D = -2 + 2i,  x%5B2%5D = -2 - 2i.

Solved.


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+%2B+4x+%2B+8+=+0+
I can complete the square to solve
+x%5E2+%2B+4x+=+-8+
+x%5E2+%2B+4x+%2B+%284%2F2%29%5E2+=+-8+%2B+%284%2F2%29%5E2+
+x%5E2+%2B+4x+%2B+4+=+-8+%2B+4+
+%28+x+%2B+2+%29%5E2+=+-4+
Take the square root of both sides
+x+%2B+2+=+sqrt%28-4%29+
+x+%2B+2+=+2i+
+x+=+-2+%2B+2i+
and, also, taking the negative square root of +-4+,
+x+%2B+2+=+-sqrt%28-4%29+
+x+%2B+2+=+-2i+
+x+=+-2+-+2i+
-----------------------
The roots are +-2+%2B+2i+ and +-2+-+2i+
---------------------------------------------
To check, you can plug either solution for +x+
back into original equation, like this:
+x%5E2+%2B+4x+%2B+8+=+0+
+%28+-2+%2B+2i+%29%5E2+%2B+4%2A%28+-2+%2B+2i+%29+%2B+8+=+0+
You can do the checks