Solve for s: $s^2 - 23s - 24 = 0$
Understand the Problem
The question asks to solve a quadratic equation for the variable 's'. We can use factoring or the quadratic formula to find the solutions for 's'.
Answer
$s = 24, -1$
Answer for screen readers
$s = 24, -1$
Steps to Solve
- Factor the quadratic equation
We need to find two numbers that multiply to -24 and add up to -23. These numbers are -24 and 1. So we can factor the quadratic equation as follows:
$$ (s - 24)(s + 1) = 0 $$
- Set each factor equal to zero
To find the solutions, we set each factor equal to zero:
$$ s - 24 = 0 \quad \text{or} \quad s + 1 = 0 $$
- Solve for s
Solve each equation for $s$:
$$ s = 24 \quad \text{or} \quad s = -1 $$
$s = 24, -1$
More Information
The solutions to the quadratic equation $s^2 - 23s - 24 = 0$ are $s = 24$ and $s = -1$. These are the values of $s$ that make the equation true.
Tips
A common mistake is to incorrectly factor the quadratic equation. Always double-check that the factors multiply back to the original equation. Another mistake is to forget to set each factor to zero and solve for $s$.
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