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