Answer
The solution set is {-2, -5}.
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 $c$. Thus, we see that $a$ is $1$, $b$ is $7$, and $c$ is $10$. Now, we can substitute these values into the equation:
$$x = \frac{-7 ± \sqrt {7^{2} - 4(1)(10)}}{2(1)}$$
We simplify exponents first, according to the order of operations:
$$x = \frac{-7 ± \sqrt {49 - 4(1)(10)}}{2(1)}$$
Now we simplify what is under the radical sign:
$$x = \frac{-7 ± \sqrt {49 - 40}}{2(1)}$$
$$x = \frac{-7 ± \sqrt {9}}{2(1)}$$
Now, we evaluate the radical:
$$x = \frac{-7 ± 3}{2(1)}$$
Now, we simplify the numerator, and we end up with two options because of the ± sign:
$$x = \frac{-4}{2(1)}$$ and $$x = \frac{-10}{2(1)}$$
Simplify the denominators:
$$x = \frac{-4}{2}$$ and $$x = \frac{-10}{2}$$
We simplify the fractions:
$$x = -2$$ and $$x = -5$$
The solution set is {-2, -5}.