Question

solve the quadratic equation ( x ^ { 2 } - 2 x + 1 = 0 ) by factoring. if there is more than one correct answer, enter a comma separated list.
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Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \(x^{2}-2x + 1=0\), we use the formula \((a - b)^2=a^{2}-2ab + b^{2}\). Here \(a=x\) and \(b = 1\), so \(x^{2}-2x + 1=(x - 1)^2\).
The equation becomes \((x - 1)^2=0\).

Step2: Solve for \(x\)

Take the square root of both sides: \(\sqrt{(x - 1)^2}=\sqrt{0}\).
Since \(\sqrt{(x - 1)^2}=\vert x - 1\vert\) and \(\sqrt{0}=0\), we have \(x-1 = 0\).
Adding \(1\) to both sides gives \(x=1\).

Answer:

\(1\)