Question

solve for y.
\\( y^2 - 6y - 7 = 0 \\)
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
\\( y = \square \\)

Explanation:

Step1: Factor the quadratic equation

We find two numbers that multiply to $-7$ and add to $-6$: $-7$ and $1$.
$y^2 - 6y - 7 = (y - 7)(y + 1) = 0$

Step2: Set each factor to zero

Solve for $y$ in each factor.
$y - 7 = 0$ or $y + 1 = 0$

Step3: Solve for y in each equation

Isolate $y$ for each case.
$y = 7$ or $y = -1$

Answer:

$7, -1$