Question

solve for g.
\\( g^2 + 20g - 21 = 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: Factor the quadratic equation

We need two numbers that multiply to $-21$ and add to $20$. These numbers are $21$ and $-1$.
$g^2 + 20g - 21 = (g + 21)(g - 1) = 0$

Step2: Set each factor to zero

For the product of factors to be zero, at least one factor must be zero.
$g + 21 = 0$ or $g - 1 = 0$

Step3: Solve for $g$

Solve each linear equation separately.
$g = -21$ or $g = 1$

Answer:

$g = 1, -21$