Solving a quadratic equation by factoring

The solution shown in the image is partially correct. Let’s break down the problem and find all solutions.

Given the equation:

We can factor out an x:

This equation is satisfied if either of the factors is equal to zero. So, we have two possible solutions:

Therefore, the solutions are and . The image only shows and misses the solution . Dividing both sides of the original equation by is only valid if . Since is a possible solution, this division step is incorrect and leads to missing one of the solutions.

So, the statement that the image represents the complete and correct solution is false.