Question

solve for g.
$g^2 - 24g + 144 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$g = \square$

Explanation:

Step1: Recognize the quadratic form

The equation \( g^2 - 24g + 144 = 0 \) is a quadratic equation. We can try to factor it. We need two numbers that multiply to \( 144 \) and add up to \( -24 \). Those numbers are \( -12 \) and \( -12 \) because \( (-12)\times(-12)=144 \) and \( (-12)+(-12)=-24 \).
So, the equation can be factored as \( (g - 12)(g - 12)=0 \) or \( (g - 12)^2 = 0 \).

Step2: Solve for \( g \)

If \( (g - 12)^2 = 0 \), then taking the square root of both sides, we get \( g - 12 = 0 \).
Adding \( 12 \) to both sides gives \( g = 12 \).

Answer:

\( 12 \)