Answer
$x = \dfrac{-7 ± \sqrt {17}}{2}$
Work Step by Step
Rewrite the equation in quadratic form, which is given by the formula $ax^2 + bx + c = 0$:
$x^2 + 7x + 8 = 0$
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, $a = 1$, $b = 7$, and $c = 8$.
Plug these values into the Quadratic Formula:
$x = \dfrac{-7 ± \sqrt {7^2 - 4(1)(8)}}{2(1)}$
$x = \dfrac{-7 ± \sqrt {49 - 4(1)(8)}}{2(1)}$
$x = \dfrac{-7 ± \sqrt {49 - 32}}{2}$
$x = \dfrac{-7 ± \sqrt {17}}{2}$
