Answer
$x = \dfrac{-1 ± \sqrt {17}}{8}$
Work Step by Step
Rewrite the equation in quadratic form, which is given by the formula $ax^2 + bx + c = 0$:
$4x^2 + x - 1 = 0$
We are asked to solve this quadratic equation using the Quadratic Formula, which is given as:
$x = \dfrac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the squared term, $b$ is the coefficient of the linear term, and $c$ is the constant term.
In this exercise, $a = 4$, $b = 1$, and $c = -1$.
Plug these values into the Quadratic Formula:
$x = \dfrac{-1 ± \sqrt {1^2 - 4(4)(-1)}}{2(4)}$
$x = \dfrac{-1 ± \sqrt {1 - 4(4)(-1)}}{2(4)}$
$x = \dfrac{-1 ± \sqrt {1 + 16}}{8}$
$x = \dfrac{-1 ± \sqrt {17}}{8}$
