Hey, I don't understand this question I have honestly done this question about a good 3 times but never seemed to get the right answer. Please Help!!!
Solve each equation by factoring. Check your answers. 7x^2=21x
7x^2 = 21x
7x^2-21x = 0
7x(x-3) = 0
This is why we always set stuff to zero. If the product of factors is zero, one of the factors must be zero. So, we have
7=0: never
x=0: x=0
x-3 = 0: x=3
Those are the solutions: x = 0 or 3
Sure! I'd be happy to help you with this equation. To solve it by factoring, we need to set the equation equal to zero and then factor out any common factors.
Let's start by rearranging the equation to have zero on one side:
7x^2 - 21x = 0
Now, let's factor out the common factor, which is x:
x(7x - 21) = 0
Now we have a product of two expressions equal to zero. In order for this product to be zero, at least one of the factors must be zero.
Factor 1: x = 0
Factor 2: 7x - 21 = 0
Solving Factor 2:
7x - 21 = 0
Adding 21 to both sides:
7x = 21
Dividing both sides by 7:
x = 3
Therefore, the solutions to the equation 7x^2 = 21x are x = 0 and x = 3.
To check our solutions, we substitute these values back into the original equation and see if the equation holds true for both solutions.
When x = 0:
7(0)^2 = 21(0)
0 = 0 [True]
When x = 3:
7(3)^2 = 21(3)
63 = 63 [True]
Both solutions satisfy the original equation, so our answers are correct.