Question

Use factoring to solve the equation.
bsquaredminus5bminus36 ​= 0
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Part 1
The solution is bequals
  
enter your response here.

Answer 1

To solve the equation \( b^2 - 5b - 36 = 0 \) by factoring, we need to find two numbers that multiply to \(-36\) (the constant term) and add to \(-5\) (the coefficient of the linear term \(b\)).

The numbers that satisfy these conditions are \(-9\) and \(4\), since:

- \(-9 \times 4 = -36\)
- \(-9 + 4 = -5\)

Now we can factor the quadratic expression:

\[
b^2 - 5b - 36 = (b - 9)(b + 4) = 0
\]

Next, we set each factor equal to zero:

1. \(b - 9 = 0\) ⟹ \(b = 9\)
2. \(b + 4 = 0\) ⟹ \(b = -4\)

Thus, the solutions to the equation are:

\[
b = 9 \quad \text{and} \quad b = -4
\]

You can enter your response as:

- **One solution is** \( b = 9 \)
- **The other solution is** \( b = -4 \)

If the response requires just one of the solutions, you can enter either \( 9 \) or \( -4 \).