Question

using the quadratic formula to solve $11x^2 - 4x = 1$, what are the values of $x$?
$\frac{2}{11}\pm\frac{\sqrt{15}}{11}$
$\frac{2}{11}\pm\frac{2\sqrt{15}}{11}$
$\frac{2}{11}\pm\frac{\sqrt{7}}{11}$
$\frac{2}{11}\pm\frac{\sqrt{7}i}{11}$

Explanation:

Step1: Rewrite to standard form

$11x^2 - 4x - 1 = 0$

Step2: Identify a, b, c

$a=11,\ b=-4,\ c=-1$

Step3: Compute discriminant

$\Delta = b^2 - 4ac = (-4)^2 - 4(11)(-1) = 16 + 44 = 60$

Step4: Simplify square root of discriminant

$\sqrt{\Delta} = \sqrt{60} = 2\sqrt{15}$

Step5: Apply quadratic formula

$x = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{4 \pm 2\sqrt{15}}{22}$

Step6: Simplify the fraction

$x = \frac{2 \pm \sqrt{15}}{11} = \frac{2}{11} \pm \frac{\sqrt{15}}{11}$

Answer:

$\frac{2}{11} \pm \frac{\sqrt{15}}{11}$ (the first option)