https://file.aiquickdraw.com/mathbot/file/1726610735727unhx8iix.jpg

The given equation is:

\[
c^2 - 10c = 0
\]

This can be factored as:

\[
c(c - 10) = 0
\]

Setting each factor equal to zero:

1. \( c = 0 \)
2. \( c - 10 = 0 \implies c = 10 \)

Thus, the solutions to the equation are \( c = 0 \) and \( c = 10 \).

Looking at the answer choices provided in the image:
- a. \( 1, -\sqrt{10} \)
- b. \( 0, -10 \)
- c. \( 0, \sqrt{10} \)
- d. \( 0, 10 \)

The correct solution corresponds to **option d**: \( 0, 10 \).

Would you like further clarification or more details?

Here are 5 related questions for practice:
1. How do you factor a quadratic equation like \( c^2 - 10c = 0 \)?
2. What are the steps to solve a quadratic equation by factoring?
3. Why is the square root of 10 incorrect in this case?
4. What method can be used to verify solutions to a quadratic equation?
5. How do you determine which roots are real or complex?

**Tip**: Always check if the quadratic can be factored easily before attempting more complex methods like the quadratic formula.

Solve the quadratic equation c^2 - 10c = 0.

Learn how to solve the quadratic equation c^2 - 10c = 0 by factoring. This example demonstrates key algebraic concepts and provides a step-by-step approach to finding the correct roots. Suitable for students in Grades 7-10.

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