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The equation given is:

\[
36x^2 + 7 = 35
\]

To solve for \( x \), follow these steps:

### Step 1: Subtract 7 from both sides
\[
36x^2 + 7 - 7 = 35 - 7
\]
\[
36x^2 = 28
\]

### Step 2: Divide both sides by 36
\[
x^2 = \frac{28}{36}
\]
\[
x^2 = \frac{7}{9}
\]

### Step 3: Take the square root of both sides
\[
x = \pm \sqrt{\frac{7}{9}}
\]

### Step 4: Simplify the square root
\[
x = \pm \frac{\sqrt{7}}{3}
\]

Thus, the solutions are:
\[
x = \frac{\sqrt{7}}{3} \quad \text{or} \quad x = -\frac{\sqrt{7}}{3}
\]

Would you like more details or clarifications?

Here are 5 related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What are the conditions for a quadratic equation to have real solutions?
3. How do you simplify square roots?
4. What happens if the discriminant in a quadratic equation is negative?
5. How do you solve quadratic equations by completing the square?

**Tip:** Always check if a quadratic equation can be factored before applying more complex methods.

Learn how to solve the quadratic equation 36x^2 + 7 = 35 with a detailed step-by-step guide. This problem covers key algebraic concepts, including solving quadratics by isolating terms and simplifying square roots. Suitable for students in Grades 8-10.

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