Which equation is related to StartRoot x + 10 EndRoot minus 1 = x?
x + 10 = x2 + x + 1
x + 10 = x2 + 2x + 1
x + 10 = x2 + 1
x + 10 = x2 – 1

The given equation is:

\[
\sqrt{x + 10} - 1 = x
\]

### Step 1: Isolate the square root term
To isolate the square root term, add 1 to both sides:

\[
\sqrt{x + 10} = x + 1
\]

### Step 2: Square both sides
Now, square both sides of the equation to eliminate the square root:

\[
(\sqrt{x + 10})^2 = (x + 1)^2
\]

This simplifies to:

\[
x + 10 = (x + 1)^2
\]

### Step 3: Expand the right-hand side
Expand \( (x + 1)^2 \):

\[
(x + 1)^2 = x^2 + 2x + 1
\]

Now the equation becomes:

\[
x + 10 = x^2 + 2x + 1
\]

Thus, the correct equation is:

\[
x + 10 = x^2 + 2x + 1
\]

So the related equation is:

**\( x + 10 = x^2 + 2x + 1 \)**

Would you like further details on how to solve the resulting quadratic equation?

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Here are 5 related questions:
1. How do you solve the quadratic equation \( x^2 + 2x - 9 = 0 \)?
2. What happens if \( x + 1 \) is replaced with \( x - 1 \)?
3. How do you simplify expressions with square roots in equations?
4. What are the steps for completing the square?
5. How does squaring both sides of an equation affect solutions?

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

Which equation is related to StartRoot x + 10 EndRoot minus 1 = x?
x + 10 = x^2 + x + 1
x + 10 = x^2 + 2x + 1
x + 10 = x^2 + 1
x + 10 = x^2 – 1

Explore how to solve the equation √(x + 10) - 1 = x, which leads to the quadratic equation x^2 + 2x + 1. Learn about isolating square roots, expanding binomials, and solving quadratic equations. This problem is designed for students in Grades 8-10.

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