When 10 b = 5 (StartRoot c EndRoot + 2) is solved for c, one equation is c = (2b minus 2) squared Which of the following is an equivalent equation to find c?


We are given the equation \( 10b = 5(\sqrt{c} + 2) \) and need to solve for \( c \).

### Step-by-step Solution:

1. **Start with the original equation:**
   \[
   10b = 5(\sqrt{c} + 2)
   \]
2. **Divide both sides by 5 to simplify:**
   \[
   2b = \sqrt{c} + 2
   \]
3. **Subtract 2 from both sides:**
   \[
   2b - 2 = \sqrt{c}
   \]
4. **Square both sides to eliminate the square root:**
   \[
   (2b - 2)^2 = c
   \]

Thus, the equation we have for \( c \) is:
\[
c = (2b - 2)^2
\]

This matches the given equation, so any equivalent equation must represent the same steps.

### Equivalent equation:
Another equivalent form could be:
\[
c = 4(b - 1)^2
\]

This equation comes from factoring and expanding the expression \( (2b - 2)^2 \).

Let me know if you would like to dive deeper into any part of this solution!

### Relative questions:
1. How do you simplify expressions involving square roots?
2. What are the steps to solve equations involving radicals?
3. How can you expand \( (2b - 2)^2 \)?
4. What techniques are useful in solving quadratic equations?
5. How does squaring both sides of an equation affect its solution?

**Tip:** Always check for extraneous solutions when squaring both sides of an equation, as it can introduce non-valid answers.

When 10b = 5(√c + 2) is solved for c, one equation is c = (2b - 2)^2. Which of the following is an equivalent equation to find c?

Learn how to solve for c in the equation 10b = 5(√c + 2) with detailed steps. This problem covers algebraic concepts including simplifying square roots, squaring both sides, and quadratic expressions. Suitable for students in Grades 8-10.

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