Question

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Part 1
Solve the equation using the quadratic formula.
x squared plus 7 x plus 10 equals 0
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Part 1
The solution set is StartSet nothing EndSet
  
.
​(Simplify your answer. Type an exact​ answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( x^2 + 7x + 10 = 0 \) using the quadratic formula, we will first identify the coefficients \( a \), \( b \), and \( c \).

In this equation:
- \( a = 1 \)
- \( b = 7 \)
- \( c = 10 \)

The quadratic formula is given by:

\[
x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a}
\]

Now, substituting the values of \( a \), \( b \), and \( c \) into the formula:

1. Calculate the discriminant \( b^2 - 4ac \):

\[
b^2 = 7^2 = 49
\]
\[
4ac = 4 \cdot 1 \cdot 10 = 40
\]
\[
b^2 - 4ac = 49 - 40 = 9
\]

2. Now plug the values into the quadratic formula:

\[
x = \frac{{-7 \pm \sqrt{9}}}{2 \cdot 1}
\]
\[
x = \frac{{-7 \pm 3}}{2}
\]

3. This gives us two potential solutions:

\[
x_1 = \frac{{-7 + 3}}{2} = \frac{{-4}}{2} = -2
\]

\[
x_2 = \frac{{-7 - 3}}{2} = \frac{{-10}}{2} = -5
\]

Thus, the solution set is:

\[
\{-2, -5\}
\]

This means the complete answer is:

\(-2, -5\)