Solving a quadratic equation by factoring

Published on November 11, 2024

Algebra

The equation x^2 - 2x = 0 has two solutions, x = 0 and x = 2, not just x = 2.

Question

true or false?

Answer

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:

Adding 2 to both sides gives

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.

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