Solve the equation by factoring. Check your answer.

Question

4x^2=8x

Answer 1

To solve the equation by factoring, we want to set the equation equal to zero. Thus, we have:

4x^2 - 8x = 0.

Next, we can factor out a common factor of 4x:

4x(x - 2) = 0.

Now, we can set each factor equal to zero and solve for x:

4x = 0 OR x - 2 = 0.

If 4x = 0, then x = 0.

If x - 2 = 0, then x = 2.

To check our answer, we substitute the values of x back into the original equation:

4(0)^2 = 8(0)

0 = 0

This equation holds true when x = 0.

4(2)^2 = 8(2)

16 = 16

This equation also holds true when x = 2.

Therefore, our solution is x = 0 or x = 2.