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 is equal to 10 and x is equal to 30 are solutions. - incorrect

Neither x=10
nor x=30
is a solution.
Neither x is equal to 10 nor x is equal to 30 is a solution. - no response given

Only x=10
is a solution.
Only x is equal to 10 is a solution. - no response given

Only x=30
is a solution.

Answer 1

To determine if 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 check if both sides are equal.

1. **Checking \( x = 10 \)**:
\[
(10 - 27)(10 - 10) = ( -17)(0) = 0
\]
The left side equals \( 0 \) while the right side is \( 60 \). Therefore, \( x = 10 \) is **not a solution**.

2. **Checking \( x = 30 \)**:
\[
(30 - 27)(30 - 10) = (3)(20) = 60
\]
The left side equals \( 60 \), which matches the right side. Therefore, \( x = 30 \) **is a solution**.

In conclusion, the only solution is \( x = 30 \).

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