Question

Solve for g.
g2+9g+20=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 \( g^2 + 9g + 20 = 0 \), we can factor the equation.

We need to find two numbers that multiply to \( 20 \) (the constant term) and add up to \( 9 \) (the coefficient of the linear term). The numbers that work are \( 4 \) and \( 5 \).

Thus, we can factor the equation as:

\[
(g + 4)(g + 5) = 0
\]

Next, we set each factor equal to zero:

1. \( g + 4 = 0 \)
\[
g = -4
\]

2. \( g + 5 = 0 \)
\[
g = -5
\]

So the solutions for \( g \) are:

\[
\boxed{-4, -5}
\]