square root 3x-4= square root 2x+9 in radical form

To solve the equation \(\sqrt{3x - 4} = \sqrt{2x + 9}\), let's proceed step by step:

### Step 1: Square both sides
We begin by squaring both sides to eliminate the square roots:

\[
(\sqrt{3x - 4})^2 = (\sqrt{2x + 9})^2
\]

This simplifies to:

\[
3x - 4 = 2x + 9
\]

### Step 2: Isolate the variable \(x\)
Now, subtract \(2x\) from both sides:

\[
3x - 2x - 4 = 9
\]

This simplifies to:

\[
x - 4 = 9
\]

### Step 3: Solve for \(x\)
Add 4 to both sides:

\[
x = 13
\]

### Step 4: Check the solution
We substitute \(x = 13\) back into the original equation to verify:

\[
\sqrt{3(13) - 4} = \sqrt{2(13) + 9}
\]

Simplify both sides:

\[
\sqrt{39 - 4} = \sqrt{26 + 9}
\]
\[
\sqrt{35} = \sqrt{35}
\]

Since both sides are equal, \(x = 13\) is the correct solution.

Would you like more details or have any questions?

Here are 5 questions that expand on this topic:
1. How do you solve radical equations with higher powers?
2. What happens if squaring introduces extraneous solutions?
3. Can you solve for \(x\) if the radicals differ in form?
4. How do you handle equations involving multiple radicals?
5. What techniques simplify radicals with variables?

**Tip:** Always check for extraneous solutions when solving radical equations by substituting the solution back into the original equation.

Discover how to solve the radical equation √(3x - 4) = √(2x + 9) with our detailed step-by-step solution. This guide covers key algebraic concepts, including squaring to eliminate radicals and solving basic linear equations, suitable for students in Grades 8-10.

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