Question

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

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

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

Only x=30 is a solution.
Only x equals 30 is a solution.

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

Answer 1

To determine whether the values \( x = 10 \) and \( x = 30 \) are solutions to the quadratic equation \((x - 27)(x - 10) = 60\), we can substitute these values into the equation and check if they satisfy it.

1. **Testing \( x = 10 \)**:
\[
(10 - 27)(10 - 10) = (-17)(0) = 0
\]
Since \( 0 \neq 60 \), \( x = 10 \) is **not** a solution.

2. **Testing \( x = 30 \)**:
\[
(30 - 27)(30 - 10) = (3)(20) = 60
\]
Since \( 60 = 60 \), \( x = 30 \) **is** a solution.

Based on our findings, only \( x = 30 \) is a solution.

Therefore, the correct response is:
**Only \( x = 30 \) is a solution.**