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.

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

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

Only x=30 is a solution.

Answer 1

To determine if \( x = 10 \) and \( x = 30 \) are solutions to the quadratic equation \( (x - 27)(x - 10) = 60 \), we will substitute each value into the equation and see if the equation holds true.

1. **Test \( x = 10 \)**:
\[
(10 - 27)(10 - 10) = 60
\]
\[
(-17)(0) = 60
\]
\[
0 = 60
\]
This is false, so \( x = 10 \) is **not a solution**.

2. **Test \( x = 30 \)**:
\[
(30 - 27)(30 - 10) = 60
\]
\[
(3)(20) = 60
\]
\[
60 = 60
\]
This is true, so \( x = 30 \) **is a solution**.

In conclusion, the correct response is:

**Only \( x = 30 \) is a solution.**