Determine whether the values 10 and 30 are solutions to the quadratic equation (x – 27)(x – 10) = 60.
• Only x = 10 is a solution
• Only x = 30 is a solution
• Both x = 10 and x = 30 are solutions.
• Neither x = 10 and x = 30 are solutions.
To check whether 10 and 30 are solutions to the quadratic equation (x – 27)(x – 10) = 60, we need to substitute these values into the equation and see if both sides are equal.
For x = 10:
(10 - 27)(10 - 10) = 60
(-17)(0) = 60
0 = 60
The equation is not satisfied for x = 10, so x = 10 is not a solution.
For x = 30:
(30 - 27)(30 - 10) = 60
(3)(20) = 60
60 = 60
The equation is satisfied for x = 30, so x = 30 is a solution.
Therefore, only x = 30 is a solution to the quadratic equation, so the correct answer is: Only x = 30 is a solution.