Question

solve for w.

$w^2 - 2w + 1 = 0$

if there is more than one solution, separate them with commas
if there is no solution, click on
o solution\.

Explanation:

Step1: Factor the quadratic equation

The quadratic equation \( w^2 - 2w + 1 = 0 \) can be factored using the perfect square trinomial formula \( a^2 - 2ab + b^2=(a - b)^2 \). Here, \( a = w \) and \( b = 1 \), so the equation factors to \( (w - 1)^2 = 0 \).

Step2: Solve for \( w \)

Taking the square root of both sides of \( (w - 1)^2 = 0 \), we get \( w - 1 = 0 \). Adding 1 to both sides gives \( w = 1 \). Since the square of a number is zero only when the number itself is zero, this is a repeated root.

Answer:

\( 1 \)