Solve 2q^2 - 4q = 0
Understand the Problem
The question asks to solve the quadratic equation 2q^2 - 4q = 0 for the variable q. This can be done by factoring out a common term and then setting each factor equal to zero to find the solutions.
Answer
$q = 0, 2$
Answer for screen readers
$q = 0, 2$
Steps to Solve
- Factor out the common term
The equation is $2q^2 - 4q = 0$. We can factor out $2q$ from both terms.
$$2q(q - 2) = 0$$
- Set each factor equal to zero
Now, we set each factor equal to zero and solve for $q$.
$$2q = 0$$ $$q - 2 = 0$$
- Solve for $q$ in each case
For the first equation, divide both sides by 2:
$$q = \frac{0}{2} = 0$$
For the second equation, add 2 to both sides:
$$q = 2$$
$q = 0, 2$
More Information
The given quadratic equation has two solutions, $q = 0$ and $q = 2$.
Tips
A common mistake is to divide the original equation by $q$ before factoring. While this can lead to the solution $q=2$, it causes you to lose the solution $q=0$ because you are effectively dividing by zero when $q=0$. Factoring is the preferred method.
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