Question

Solve for g.
g2+14g+13=0
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
g=

Answer 1

To solve the quadratic equation \( g^2 + 14g + 13 = 0 \), we can use the quadratic formula:

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

For the given equation, we identify the coefficients as follows:
- \( a = 1 \)
- \( b = 14 \)
- \( c = 13 \)

Next, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 = 14^2 = 196
\]
\[
4ac = 4 \cdot 1 \cdot 13 = 52
\]
\[
b^2 - 4ac = 196 - 52 = 144
\]

Now we plug the values into the quadratic formula:

\[
g = \frac{-14 \pm \sqrt{144}}{2 \cdot 1}
\]
\[
g = \frac{-14 \pm 12}{2}
\]

This will give us two possible solutions for \( g \):

1. Using the \( + \) sign:
\[
g = \frac{-14 + 12}{2} = \frac{-2}{2} = -1
\]

2. Using the \( - \) sign:
\[
g = \frac{-14 - 12}{2} = \frac{-26}{2} = -13
\]

Thus, the solutions for \( g \) are:

\[
g = -1, -13
\]

So the final answer is:

\[
g = -1, -13
\]