Question

How do you solve $2x={{x}^{2}}$?

Answer 1

Hint: We will write the given equation in the standard form. Then we will factorize the given equation. For factoring, we will take common one factor from both the terms. We will do this until we have a product of two terms as the given equation. Then we will solve the factored equation to obtain the possible values of $x$.

Complete step-by-step solution:
The given equation is $2x={{x}^{2}}$. We can rewrite the given equation in the standard form as follows,
${{x}^{2}}-2x=0$
Now, to solve this equation, we will use the method of factorization. For factorization, we will take out a common factor from both the terms in the given equation. From the given equation, we can see that both the terms in the equation are divisible by $x$. So, we can take $x$ as a common factor from both the terms of the given equation. Hence, we have the following,
$x\left( x-2 \right)=0$
Next, we have to solve the above equation. We can see that we have two possibilities. The first possibility is that $x=0$ and the second possibility is $x-2=0$. Therefore, the roots of the given equation are $x=0$ and $x=2$.

Note: We used the method of factorization to solve the given equation. There are other methods which can be used to solve the equation. These methods are using quadratic formulas or completing the square. We can choose the method based on our convenience and easier calculations. We can further study the given quadratic equation by plotting its graph, which is a parabola.