Answer
$x = \frac{7}{2}$ or $x = -9$
Work Step by Step
The quadratic equation is one that is in the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are real numbers.
We are asked to solve the quadratic equation given using the quadratic formula, which is given by the formula:
$x = \frac{-b ± \sqrt {b^2 - 4ac}}{2a}$
Let's plug our values into this formula to solve for $x$:
$x = \frac{-11 ± \sqrt {(11)^2 - 4(2)(-63)}}{2(2)}$
Let's simplify:
$x = \frac{-11 ± \sqrt {121 + 504}}{4}$
Simplify what is under the radical sign:
$x = \frac{-11 ± \sqrt {625}}{4}$
Evaluate the square root:
$x = \frac{-11 ± 25}{4}$
Simplify the numerator:
$x = \frac{14}{4}$ or $x = \frac{-36}{4}$
Simplify the fractions:
$x = \frac{7}{2}$ or $x = -9$
