https://file.aiquickdraw.com/mathbot/file/17272360007190x2rc9vv.jpg

The equation in the image is:

\[
2x - x^2 = 1
\]

This is a quadratic equation. To solve it, we can rearrange it into the standard form \( ax^2 + bx + c = 0 \).

### Steps to solve:

1. Rearrange the equation:
   \[
   -x^2 + 2x - 1 = 0
   \]
   Multiply the entire equation by \(-1\) to simplify:
   \[
   x^2 - 2x + 1 = 0
   \]

2. Now we have the equation \( x^2 - 2x + 1 = 0 \). This can be factored as:
   \[
   (x - 1)^2 = 0
   \]

3. Solve for \( x \):
   \[
   x - 1 = 0
   \]
   \[
   x = 1
   \]

Thus, the solution is \( x = 1 \).

Would you like further details or have any questions?

Here are five related questions you could explore:
1. How do you solve quadratic equations using the quadratic formula?
2. What are the different methods of solving quadratic equations (e.g., completing the square)?
3. What are the characteristics of a quadratic equation with a double root?
4. How do you graph quadratic functions, and what does the vertex represent?
5. Can quadratic equations always be factored, and what if they cannot?

**Tip:** Always check if a quadratic can be factored easily before using other methods like the quadratic formula.

Solve the quadratic equation 2x - x^2 = 1

Learn how to solve the quadratic equation 2x - x^2 = 1 with a detailed step-by-step solution. This problem demonstrates key algebraic concepts such as factoring and the standard form of quadratic equations, suitable for students in Grades 8-10.

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