# How do you solve 2x^2 - 12x + 10 = 0?

Nov 4, 2015

The two solutions are $x = 1$ and $x = 5$.

#### Explanation:

First of all, we can divide both members by $2$:

$\frac{2 {x}^{2} - 12 x + 10}{2} = \frac{0}{2}$

which simplifies into

${x}^{2} - 6 x + 5 = 0$

Arrived at this point, we can complete the square:

${x}^{2} - 6 x + 9 - 9 + 5 = 0$

And we notice that ${x}^{2} - 6 x + 9 = {\left(x - 3\right)}^{2}$.

So, the whole expression becomes

${\left(x - 3\right)}^{2} - 4 = 0$

$\setminus \iff$

${\left(x - 3\right)}^{2} = 4$

$\setminus \iff$

$x - 3 = \setminus \pm 2$

$\iff$

$x = 3 \setminus \pm 2 \setminus \implies x = 1$ or $x = 5$.