Solve by factoring.z squared plus 4 z minus 45equals0Question content area bottomPart 1zequalsenter your response here ​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \( z^2 + 4z - 45 = 0 \) by factoring, we need to find two numbers that multiply to \(-45\) (the constant term) and add to \(4\) (the coefficient of the linear term).

The numbers that satisfy these conditions are \(9\) and \(-5\) because:

• \(9 \times (-5) = -45\)
• \(9 + (-5) = 4\)

Now, we can factor the quadratic expression:

\[ z^2 + 4z - 45 = (z + 9)(z - 5) = 0 \]

Next, we set each factor equal to zero:

1. \( z + 9 = 0 \)
   \( z = -9 \)

2. \( z - 5 = 0 \)
   \( z = 5 \)

So the solutions to the equation \( z^2 + 4z - 45 = 0 \) are:

\[ z = -9, 5 \]

Thus, the answer is:

\(-9, 5\)