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

Oct 5, 2015

color(blue)(x=1 is the solution for the equation.

#### Explanation:

x^2−2x+1=0

We can Split the Middle Term of this expression to factorise it and thereby find the solutions.

In this technique, if we have to factorise an expression like $a {x}^{2} + b x + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 1 \cdot 1 = 1$
and
${N}_{1} + {N}_{2} = b = - 2$

After trying out a few numbers we get ${N}_{1} = - 1$ and ${N}_{2} = - 1$
$- 1 \cdot - 1 = 1$, and $\left(- 1\right) + \left(- 1\right) = - 2$

x^2−color(blue)(2x)+1=x^2−color(blue)(1x-1x)+1

$= x \left(x - 1\right) - 1 \left(x - 1\right)$

$\left(x - 1\right) \left(x - 1\right)$ , is the factorised form of the expression.

We now equate the factor to zero(both factors are equal).

$x - 1 = 0 , x = 1$
color(blue)(x=1 is the solution for the equation.