# How do you solve 2x^2 - 11x + 5 = 0?

Jul 10, 2015

The solutions for the equation are:
color(blue)(x=1/2, x=5

#### Explanation:

$2 {x}^{2} - 11 x + 5 = 0$

We can first factorise the equation by splitting the middle term and then find the solutions:

$2 {x}^{2} - \textcolor{b l u e}{11 x} + 5 = 0$

$2 {x}^{2} \textcolor{b l u e}{- 10 x - 1 x} + 5 = 0$

$2 x \left(x - 5\right) - 1 \left(x - 5\right) = 0$

color(blue)((2x - 1)(x-5) = 0

Now we equate each of the two terms with zero to find the solutions:
$\textcolor{b l u e}{2 x - 1 = 0 , x = \frac{1}{2}}$

color(blue)(x-5=0, x=5