Let's solve the equation \( 2x^2 - 50 = 0 \).

### Step 1: Move the constant to the other side
\[
2x^2 = 50
\]

### Step 2: Divide both sides by 2
\[
x^2 = 25
\]

### Step 3: Take the square root of both sides
\[
x = \pm \sqrt{25}
\]

### Step 4: Simplify the square root
\[
x = \pm 5
\]

Thus, the solution is:
\[
x = 5 \quad \text{or} \quad x = -5
\]

Would you like more details on any of these steps or have any further questions?

Here are five related questions for practice:
1. Solve \( 3x^2 - 27 = 0 \).
2. Solve \( x^2 - 16 = 0 \).
3. Solve \( 4x^2 - 36 = 0 \).
4. Solve \( 5x^2 - 125 = 0 \).
5. Solve \( x^2 + 49 = 0 \).

**Tip:** Always isolate the squared term first when solving quadratic equations of the form \( ax^2 + c = 0 \).

Master solving the quadratic equation 2x^2 - 50 = 0 with this detailed solution. Learn how to isolate the variable, apply square roots, and understand key algebra concepts. Suitable for students in Grades 8-10.

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