How do I do this? Thank you for your help in advance!

2x^{2} - 4x + 6 = 0 by completing the square.

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Our problem

2x^2-4x+6=0

First notice that each of the coefficients are divisible by 2. So first divide by 2

x^2-2x+3=0

Now, move the 3 from the left hand side, to the right hand side. Since on the left is addition, we need to subtract the three from both sides

x^2-2x=-3

Next, you divide the coefficient in front of the x term, and then square it

Our coefficient is -2.

(-2/2)^2= 1

Therefore, we add 1 to both sides

x^2-2x+1=-3+1

Now, we find multiples of 1 that will give add up to -2.

Well -1x-1=1, and -1+-1=-2. Therefore

(x-1)^2=-2

Square root both sides

x-1= square root of -2 (which is not possible so....)

x-1= +/- square root of -1 multiplied by 2

x-1= i +/- multiplied by square root of 2

x=i multiplied by +/-square root of 2 +1

Remember, that i means it is an imaginary number!

Please let me know if you would like to see this written on paper, and then a photo taken of it.

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