Question

solve for d.
$d^2 - 12d - 13 = 0$
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
$d = $

Explanation:

Step1: Factor the quadratic equation

We find two numbers that multiply to $-13$ and add to $-12$. These numbers are $-13$ and $1$.
$d^2 - 12d - 13 = (d - 13)(d + 1) = 0$

Step2: Set each factor equal to 0

Solve for $d$ in each resulting equation.
$d - 13 = 0$ or $d + 1 = 0$

Step3: Solve for d in each equation

For $d - 13 = 0$, add 13 to both sides: $d = 13$.
For $d + 1 = 0$, subtract 1 from both sides: $d = -1$.

Answer:

$d = 13, -1$