SOLUTION: Solve by completing the square x^2 + 2 = 2x

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Question 58198This question is from textbook Elementary and Intermediate Algebra
: Solve by completing the square
x^2 + 2 = 2x
This question is from textbook Elementary and Intermediate Algebra

Found 2 solutions by funmath, Earlsdon:
Answer by funmath(2925) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square
x%5E2%2B2=2x
x%5E2-2x%2B2=0
x%5E2-2x%2B2-2=0-2
x%5E2-2x=-2
%28x%5E2-2x%2B1%29=-2%2B1
%28x-1%29%5E2=-1
sqrt%28%28x-1%29%5E2%29=sqrt%28-1%29
x-1=%2B-i
x-1%2B1=1%2B-i
x=1-i and x=1+i
If you are not using imaginary numbers yet, there is no solution.
Happy Calculating!!!

Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by completing the square:
x%5E2+%2B+2+=+2x Subtact 2x from both sides.
x%5E2+-+2x+%2B+2+=+0 Subtract 2 from both sides.
x%5E2+-+2x+=+-2 Add the square of half the x-coefficient ((-2/2)^2 = 1) to both sides.
x%5E2+-+2x+%2B+1+=+-1 Factor the left side.
%28x-1%29%5E2+=+-1 Take the square root of both sides.
x-1+= +/-sqrt%28-1%29 Add 1 to both sides.
x+=+1%2Bsqrt%28-1%29 and x+=+1-sqrt%28-1%29 which you can write as:
x+=+1%2Bi and x+=+1-i Where: i+=+sqrt%28-1%29