How to factor x^2 - 2x + 4 = 0?

Feb 22, 2018

${\left(x - 1\right)}^{2} + 3 = 0$

Explanation:

Let's factor by completing the square. Our quadratic is in the form $a {x}^{2} + b x + c$. We complete the square by taking half of our $b$ value, squaring it, and adding it to both sides of the equation.

We know that $b = - 2$, Half of that is $- 1$, and squaring that gives us $1$. Let's add that to both sides. We also have to subtract $4$ from both sides so we can be able to factor. We get:

${x}^{2} - 2 x + 1 = - 4 + 1$

Simplifying, we get:

${x}^{2} - 2 x + 1 = - 3$

The left side can be factored as ${\left(x - 1\right)}^{2}$. If we add $- 1$ and $- 1$, we get $- 2$. When we multiply them, we get positive $1$.

${\left(x - 1\right)}^{2} = - 3$

Finally, we can add $3$ to both sides, and we get:

${\left(x - 1\right)}^{2} + 3 = 0$