Solve the quadratic equation 46x2−138x=0
by factoring out the GCF.(1 point)
Responses
The solutions are x=0
and x=3
.
The solutions are x equals 0 and x equals 3 .
The solutions are x=−46
and x=3
.
The solutions are x equals negative 46 and x equals 3 .
The solutions are x=0
and x=46
.
The solutions are x equals 0 and x equals 46 .
The solutions are x=−3
and x=46
.
The correct answer is: The solutions are x=0 and x=3.
To solve the quadratic equation by factoring out the GCF, we can start by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 46.
Factoring out the GCF:
46x^2 - 138x = 0
46x(x - 3) = 0
Now, we set each factor equal to zero and solve for x:
46x = 0 or x - 3 = 0
Solving the first equation:
46x = 0
Dividing both sides by 46:
x = 0
Solving the second equation:
x - 3 = 0
Adding 3 to both sides:
x = 3
Therefore, the solutions to the quadratic equation 46x^2 - 138x = 0 by factoring out the GCF are x = 0 and x = 3.
To solve the quadratic equation 46x^2 - 138x = 0 by factoring out the GCF (Greatest Common Factor), follow these steps:
Step 1: Factor out the common term, which in this case is 46x:
46x(x - 3) = 0
Step 2: Set each factor equal to zero and solve for x:
46x = 0 => x = 0
x - 3 = 0 => x = 3
Therefore, the solutions to the quadratic equation 46x^2 - 138x = 0 are x = 0 and x = 3.