Let's determine if [tex]\( x = 3 \)[/tex] is a solution to the quadratic equation [tex]\( x^2 - 11x = 24 \)[/tex].
### Step-by-Step Solution:
1. Substitute [tex]\( x = 3 \)[/tex] into the equation:
Start by substituting [tex]\( x = 3 \)[/tex] into the left-hand side of the equation:
[tex]\[
x^2 - 11x
\][/tex]
2. Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Calculate [tex]\( 11 \cdot 3 \)[/tex]:
[tex]\[
11 \cdot 3 = 33
\][/tex]
4. Substitute these values back into the expression:
[tex]\[
9 - 33
\][/tex]
5. Perform the subtraction:
[tex]\[
9 - 33 = -24
\][/tex]
6. Compare the result to the right-hand side of the equation:
The right-hand side of the equation is 24. From the calculations, we have obtained [tex]\(-24\)[/tex] on the left-hand side. Clearly,
[tex]\[
-24 \neq 24
\][/tex]
### Conclusion:
Since substituting [tex]\( x = 3 \)[/tex] into [tex]\( x^2 - 11x \)[/tex] does not equal 24, we can conclude that [tex]\( x = 3 \)[/tex] is not a solution to the equation [tex]\( x^2 - 11x = 24 \)[/tex].
