Solve for u u^2-2u+1=0

$u^{2} - 2 u + 1 = 0$

Step 1

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$u^{2} - 2 u + 1^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 u = 2 \cdot u \cdot 1$

Rewrite the polynomial.

$u^{2} - 2 \cdot u \cdot 1 + 1^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = u$ and $b = 1$ .

${(u - 1)}^{2} = 0$

Step 2

Set the $u - 1$ equal to $0$ .

$u - 1 = 0$

Step 3

Add $1$ to both sides of the equation.

$u = 1$