# How do you solve x^2 - 2x +1=0?

Jun 25, 2015

$x = 1$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXXX}}$${x}^{2} - 2 x + 1 = 0$
Factor the left side to get
$\textcolor{w h i t e}{\text{XXXX}}$$\left(x - 1\right) \left(x - 1\right) = 0$
From which it follows that
$\textcolor{w h i t e}{\text{XXXX}}$$\left(x - 1\right) = 0$
and
$\textcolor{w h i t e}{\text{XXXX}}$$x = 1$

Jun 25, 2015

This is a quadratic equation, that you can factorise.

#### Explanation:

Find a pair of numbers that add up to $- 2 x$ and multiplies to $+ 1$

Maybe you'll see that that would be $- 1 \mathmr{and} - 1$

Now you can factorise:
$= \left(x - 1\right) \cdot \left(x - 1\right) = 0 \to x - 1 = 0 \to x = 1$

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