# How do you solve 11x^2 - x - 3 = 0?

May 8, 2018

$x = \frac{1}{22} \pm \frac{1}{22} \sqrt{133}$

#### Explanation:

$\text{this quadratic does not factorise with whole number values}$

$\text{solve using the "color(blue)"quadratic formula}$

•color(white)(x)x=(-b+-sqrt(b^2-4ac))/(2a)

$11 {x}^{2} - x - 3 = 0 \leftarrow \textcolor{b l u e}{\text{is in standard form}}$

$\text{with "a=11,b=-1" and } c = - 3$

$\Rightarrow x = \frac{1 \pm \sqrt{1 + 132}}{22} = \frac{1 \pm \sqrt{133}}{22}$

$\Rightarrow x = \frac{1}{22} \pm \frac{1}{22} \sqrt{133} \leftarrow \textcolor{red}{\text{exact solutions}}$

$\Rightarrow x \approx - 0.48 \text{ or "x~~0.57" to 2 dec. places}$