Complete the Square x^2-2x+2

Problem

x^2−2*x+2

Solution

1. Identify the coefficient of the linear term x which is b=−2

2. Calculate the value needed to complete the square by taking half of b and squaring it: ((−2)/2)^2=(−1)^2=1

3. Rewrite the expression by splitting the constant term 2 into $1 + 1$ to include the required value.

4. Group the first three terms to form a perfect square trinomial: (x^2−2*x+1)+1

5. Factor the perfect square trinomial into the form (x−h)^2

Final Answer

x^2−2*x+2=(x−1)^2+1

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