https://file.aiquickdraw.com/mathbot/file/1725823897785hjhiqfpd.jpg

Let's analyze the equation from the image:

\[
\sqrt{x + 15} + \sqrt{x} = 15
\]

### Step 1: Isolate one of the square roots.
We'll subtract \(\sqrt{x}\) from both sides:

\[
\sqrt{x + 15} = 15 - \sqrt{x}
\]

### Step 2: Square both sides.
To eliminate the square roots, we square both sides of the equation:

\[
(\sqrt{x + 15})^2 = (15 - \sqrt{x})^2
\]

This simplifies to:

\[
x + 15 = (15)^2 - 2 \cdot 15 \cdot \sqrt{x} + (\sqrt{x})^2
\]

\[
x + 15 = 225 - 30\sqrt{x} + x
\]

### Step 3: Simplify the equation.
Cancel out the \(x\) on both sides:

\[
15 = 225 - 30\sqrt{x}
\]

### Step 4: Isolate the square root.
Subtract 225 from both sides:

\[
15 - 225 = -30\sqrt{x}
\]

\[
-210 = -30\sqrt{x}
\]

Now, divide both sides by -30:

\[
\sqrt{x} = \frac{210}{30} = 7
\]

### Step 5: Solve for \(x\).
Square both sides again to eliminate the square root:

\[
x = 7^2 = 49
\]

### Conclusion:
The solution is \(x = 49\).

Would you like further explanation on any step or have other questions?

---

Here are 5 related questions to expand your understanding:
1. What if there were two square root terms on the same side? How would that change the method?
2. Can you verify the solution by substituting \(x = 49\) back into the original equation?
3. What are the potential pitfalls when solving equations involving square roots?
4. How would the solution change if the equation was \(\sqrt{x + 20} + \sqrt{x} = 15\)?
5. How can you graphically represent the solution to this equation?

**Tip**: Always check your solution by substituting the value of \(x\) back into the original equation to ensure it satisfies all parts of the equation.

Learn how to solve the radical equation sqrt(x + 15) + sqrt(x) = 15 with step-by-step solutions. This covers key algebra concepts such as square roots and isolating variables. Suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation