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

Only x=10 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.

**First, let's check \( x = 10 \):**

\[
(x - 27)(x - 10) = (10 - 27)(10 - 10) = (-17)(0) = 0
\]

Since \( 0 \neq 60 \), \( x = 10 \) is not a solution.

**Next, let's check \( x = 30 \):**

\[
(x - 27)(x - 10) = (30 - 27)(30 - 10) = (3)(20) = 60
\]

Since \( 60 = 60 \), \( x = 30 \) is a solution.

**Conclusion:**

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

So the correct response is: "Only \( x = 30 \) is a solution."