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.

Only x=30
is a solution
Only x is equal to 30 is a solution

Only x=10
is a solution
Only x is equal to 10 is a solution

Neitherx=10
nor x=30
is a solution.

Answer 1

To determine whether \( x = 10 \) and \( x = 30 \) are solutions to the quadratic equation \((x - 27)(x - 10) = 60\), we can check each value by substituting them into the equation.

1. **Check \( x = 10 \)**:
\[
(10 - 27)(10 - 10) = 60
\]
\[
(-17)(0) = 60
\]
This simplifies to \( 0 = 60\), which is **not true**. So, \( x = 10 \) is **not a solution**.

2. **Check \( x = 30 \)**:
\[
(30 - 27)(30 - 10) = 60
\]
\[
(3)(20) = 60
\]
This simplifies to \( 60 = 60\), which is **true**. So, \( x = 30 \) **is a solution**.

Based on the checks, we conclude:

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

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