What are the roots of the equation x^2 -4x + 3 = 0
x^2 - 4x = 3
x^2 +2(-2)x + -2^2 = -3 = -2^2
x^2 + -4x + 4 = 1
(x + -2)^2 = 1
qrt (x+-2)^2 = sqrt 1
x+-2 = plus or minus 1
therefore x=1
x=3 roots are 1 and 3

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1. You did this about the most difficult way.

Consider:
x^2-4x-3=0
(x-1)(x-3)=0
x= 1, or 3

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2. x^2 -4x + 3 = 0
factor
(x-3)(x-1) = 0
x = 3 or x = 1
or complete the square as you tried
x^2 -4 x = -3 note sign change of 3
x^2 - 4 x + 4 = -3 +4 = 1
(x-2)^2 = 1
x = 2 +/- 1
x = 1 or x = 3

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3. I believe you are trying to factor the polynomial.
so x^2 -4x+3

(x-1)(x-3) =0
x= 1,3

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4. Alison, I am sure Sheila was trying to do it by completing the square. Note taking half of the coef. of x and squaring it. Factoring is too easy.

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5. I did do it the long way-you way is much simpler Thank you all

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