Question

solve for t.
t² - 12t - 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.
t =
submit

Explanation:

Step1: Factor the quadratic equation

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

Step2: Set each factor to zero

For the product to be zero, at least one factor is zero.
$t - 13 = 0$ or $t + 1 = 0$

Step3: Solve for t in each equation

Solve $t - 13 = 0$: $t = 13$
Solve $t + 1 = 0$: $t = -1$

Answer:

$t = 13, -1$