Answer
The solution set is {-2, -3}.
Work Step by Step
The quadratic formula is given by:
$$x = \frac{-b ± \sqrt {b^{2} - 4ac}}{2a}$$
To solve a quadratic equation by the quadratic formula, we need to know what $a$, $b$, and $c$ are. The coefficient of the first term is $a$. The coefficient of the second term is $b$. The constant term is $c$. Now, we can substitute these values into the equation:
$$x = \frac{-5 ± \sqrt {5^{2} - 4(1)(6)}}{2(1)}$$
We simplify exponents first, according to the order of operations:
$$x = \frac{-5 ± \sqrt {25 - 4(1)(6)}}{2(1)}$$
Now we simplify what is under the radical sign:
$$x = \frac{-5 ± \sqrt {25 - 24}}{2(1)}$$
$$x = \frac{-5 ± \sqrt {1}}{2(1)}$$
Now, we evaluate the radical:
$$x = \frac{-5 ± 1}{2(1)}$$
Now, we simplify the numerator, and we end up with two options because of the ± sign:
$$x = \frac{-4}{2(1)}$$ and $$x = \frac{-6}{2(1)}$$
Simplify the denominators:
$$x = \frac{-4}{2}$$ and $$x = \frac{-6}{2}$$
We simplify the fractions:
$$x = -2$$ and $$x = -3$$
The solution set is {-2, -3}.
