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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=

1 answer

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:

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