Answer
$x = \dfrac{-7 \pm \sqrt {5}}{2}$
Work Step by Step
We are asked to solve this equation using the quadratic formula, which is given by:
$x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}$
where $a$ is the coefficient of the $x^2$ term, $b$ is the coefficient of the 1st degree term, and $c$ is the constant.
The given equation has $a=1, b=7,$ and $c=11$. Substitute these into the quadratic formula to obtain:
$x = \dfrac{-7 \pm \sqrt {(7)^2 - 4(1)(11)}}{2(1)}$
$x = \dfrac{-7 \pm \sqrt {49 - 44}}{2}$
$x = \dfrac{-7 \pm \sqrt {5}}{2}$
This is the simplest form of the solution.
