Solve the equation.

StartRoot x EndRoot minus StartRoot x minus 12 EndRoot equals 2x−x−12=2




The equation you provided can be interpreted as follows:

\[
\sqrt{x} - \sqrt{x - 12} = 2
\]

We need to solve for \( x \). Here's the step-by-step solution:

### Step 1: Isolate one of the square roots

First, add \(\sqrt{x - 12}\) to both sides to isolate one of the square roots:

\[
\sqrt{x} = 2 + \sqrt{x - 12}
\]

### Step 2: Square both sides

Square both sides of the equation to eliminate the square root:

\[
(\sqrt{x})^2 = (2 + \sqrt{x - 12})^2
\]

This simplifies to:

\[
x = 4 + 4\sqrt{x - 12} + (x - 12)
\]

### Step 3: Simplify the equation

Simplify the equation by combining like terms:

\[
x = x - 8 + 4\sqrt{x - 12}
\]

Now, subtract \(x\) from both sides:

\[
0 = -8 + 4\sqrt{x - 12}
\]

### Step 4: Isolate the square root

Add 8 to both sides to isolate the square root:

\[
8 = 4\sqrt{x - 12}
\]

Now, divide both sides by 4:

\[
2 = \sqrt{x - 12}
\]

### Step 5: Square both sides again

Square both sides to eliminate the square root:

\[
4 = x - 12
\]

### Step 6: Solve for \(x\)

Add 12 to both sides:

\[
x = 16
\]

### Step 7: Verify the solution

Substitute \(x = 16\) back into the original equation to verify:

\[
\sqrt{16} - \sqrt{16 - 12} = 4 - 2 = 2
\]

Since both sides of the original equation are equal, \(x = 16\) is indeed the correct solution.

**Solution**: \(x = 16\)

Would you like more details or have any questions?

---

**Here are 5 related questions for further practice:**

1. Solve the equation \( \sqrt{x} + \sqrt{x - 4} = 6 \).
2. Solve for \(x\) in the equation \( x - \sqrt{2x + 3} = 7 \).
3. What is the solution to the equation \( \sqrt{x + 9} + \sqrt{x} = 3 \)?
4. Solve \( 3\sqrt{x} - \sqrt{x - 2} = 2 \) for \(x\).
5. Find the value of \(x\) in the equation \( \sqrt{2x + 1} = x + 3 \).

**Tip:** When dealing with square root equations, remember to check for extraneous solutions by substituting your answer back into the original equation.

Solve the equation: √x - √(x - 12) = 2

Learn how to solve the radical equation √x - √(x - 12) = 2 with a detailed step-by-step solution. This problem involves understanding algebraic concepts, properties of square roots, and isolating radicals. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation