Question

Determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60 .(1 point)
Responses

Only x=10 is a solution.
Only x equals 10 is a solution.

Both x=10 and x=30 are solutions.
Both x equals 10 and x equals 30 are solutions.

Neither x=10 nor x=30 is a solution.
Neither x equals 10 nor x equals 30 is a solution.

Only x=30 is a solution.

Answer 1

To determine whether the values \( x = 10 \) and \( x = 30 \) are solutions to the equation \( (x - 27)(x - 10) = 60 \), we can substitute each value into the equation and see if it results in a true statement.

### Check \( x = 10 \):
Substituting \( x = 10 \):
\[
(10 - 27)(10 - 10) = 60
\]
\[
(-17)(0) = 60
\]
\[
0 = 60 \quad \text{(False)}
\]
So, \( x = 10 \) is **not** a solution.

### Check \( x = 30 \):
Substituting \( x = 30 \):
\[
(30 - 27)(30 - 10) = 60
\]
\[
(3)(20) = 60
\]
\[
60 = 60 \quad \text{(True)}
\]
So, \( x = 30 \) **is** a solution.

### Conclusion:
- Only \( x = 30 \) is a solution.

The correct response is: **Only x=30 is a solution.**