hich value for \( s \) will make this equation true? \[ s(11-s)=24 \]

To find the value(s) of \( s \) that satisfy the equation: \[ s(11 - s) = 24 \] follow these steps: 1. **Expand the Equation:** \[ 11s - s^2 = 24 \] 2. **Rearrange the Equation to Standard Quadratic Form:** \[ -s^2 + 11s - 24 = 0 \] Multiply both sides by \(-1\) to make the quadratic coefficient positive: \[ s^2 - 11s + 24 = 0 \] 3. **Factor the Quadratic Equation:** We need to find two numbers that multiply to \( 24 \) (the constant term) and add up to \( -11 \) (the coefficient of \( s \)). The numbers \( -3 \) and \( -8 \) satisfy these conditions because: \[ (-3) \times (-8) = 24 \quad \text{and} \quad (-3) + (-8) = -11 \] So, the factored form is: \[ (s - 3)(s - 8) = 0 \] 4. **Solve for \( s \):** Set each factor equal to zero: \[ s - 3 = 0 \quad \Rightarrow \quad s = 3 \] \[ s - 8 = 0 \quad \Rightarrow \quad s = 8 \] 5. **Conclusion:** The values of \( s \) that make the equation true are **3** and **8**. **Verification:** - For \( s = 3 \): \[ 3(11 - 3) = 3 \times 8 = 24 \quad \text{✓} \] - For \( s = 8 \): \[ 8(11 - 8) = 8 \times 3 = 24 \quad \text{✓} \] Both solutions satisfy the original equation. **Answer:** Both \( s = 3 \) and \( s = 8 \) satisfy the equation \( s(11 - s) = 24 \).