Determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60 .(1 point)
Responses
Only x=10 is a solution.
Only x equals 10 is a solution.
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.
Both x=10 and x=30 are solutions.
To determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60, we can substitute each value into the equation and see if both sides are equal.
For x = 10:
(10−27)(10−10) = 60
(-17)(0) = 60
0 = 60
Since the equation is not true when x = 10, x=10 is not a solution.
For x = 30:
(30−27)(30−10) = 60
(3)(20) = 60
60 = 60
Since the equation is true when x = 30, x=30 is a solution.
Therefore, the correct response is:
Only x=30 is a solution.
To determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60, we can substitute these values into the equation and see if they satisfy it.
Let's check for x = 10:
Substituting x = 10 into the equation, we get:
(10−27)(10−10)=60
(-17)(0)=60
0 = 60
Since 0 does not equal to 60, x = 10 is not a solution to the equation.
Now, let's check for x = 30:
Substituting x = 30 into the equation, we get:
(30−27)(30−10)=60
(3)(20)=60
60=60
Since 60 equals 60, x = 30 is a solution to the equation.
Therefore, the correct answer is: Only x=30 is a solution.
To determine whether the values 10 and 30 are solutions to the quadratic equation (x−27)(x−10)=60, we can substitute these values into the equation and check if it holds true or not.
1. Substitute x=10 into the equation:
(10−27)(10−10)=60
(-17)(0) = 60
0 = 60
Since 0 does not equal 60, x=10 is not a solution.
2. Substitute x=30 into the equation:
(30−27)(30−10)=60
(3)(20) = 60
60 = 60
Since 60 equals 60, x=30 is a solution.
Therefore, only x=30 is a solution.