Question

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

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.
Only x equals 30 is a solution.

Both x=10 and x=30 are solutions.
Both x equals 10 and x equals 30 are solutions.
Remaining Attempts : 3

Answer 1

To determine whether the values \( x = 10 \) and \( x = 30 \) are solutions to the equation

\[
(x - 27)(x - 10) = 60,
\]

we can plug in each value into the equation and see if the equation holds true.

### Testing \( x = 10 \):

Substituting \( x = 10 \):

\[
(10 - 27)(10 - 10) = 60.
\]

This simplifies to:

\[
(-17)(0) = 60.
\]

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

### Testing \( x = 30 \):

Now, substituting \( x = 30 \):

\[
(30 - 27)(30 - 10) = 60.
\]

This simplifies to:

\[
(3)(20) = 60.
\]

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

### Conclusion:

Thus, the correct response is:

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