x²-36 we can solve by a²-b² since $ 6^2 = 36 $ but how to solve x²-35. Im absolute beginner in algebra please show me step by step 

Certainly! Let's break this down step by step.

### Problem: $ x^2 - 35 $

This expression is not a perfect square difference, unlike $ x^2 - 36 $ which can be factored using the difference of squares formula: $ a^2 - b^2 = (a + b)(a - b) $.

However, $ x^2 - 35 $ can be approached differently because 35 is not a perfect square. Here's how we can proceed:

### 1. Quadratic Equation Approach

If we are looking to solve $ x^2 - 35 = 0 $, we treat it as a quadratic equation:

\[ x^2 - 35 = 0 \]

### Step-by-Step Solution:

1. **Set the equation to zero:**
   \[ x^2 - 35 = 0 \]

2. **Isolate $ x^2 $:**
   \[ x^2 = 35 \]

3. **Take the square root of both sides:**
   \[ x = \pm \sqrt{35} \]

### Explanation:
- The symbol $ \pm $ means "plus or minus," indicating that there are two solutions to the equation.
- The square root of 35 is an irrational number, so it remains as $ \sqrt{35} $.

### Solutions:
\[ x = \sqrt{35} \]
\[ x = -\sqrt{35} \]

These are the two solutions for the equation $ x^2 - 35 = 0 $.

### 2. Factoring Approach (If possible)

If you need to factor $ x^2 - 35 $ (though it's not factorizable in the standard algebraic sense like $ x^2 - 36 $), you can write it as:

\[ x^2 - 35 = (x - \sqrt{35})(x + \sqrt{35}) \]

But this is essentially using the solutions we found earlier.

### Summary:
To solve $ x^2 - 35 $, you:
1. Set the equation equal to zero: $ x^2 - 35 = 0 $.
2. Solve for $ x^2 $: $ x^2 = 35 $.
3. Take the square root of both sides: $ x = \pm \sqrt{35} $.

This gives you the solutions $ x = \sqrt{35} $ and $ x = -\sqrt{35} $.

Do you want more details or have any questions about this process?

Here are some questions you might want to ask next:
1. How do I solve other types of quadratic equations?
2. What is the difference between a rational and an irrational number?
3. How can I factor quadratic equations?
4. What are some methods to solve quadratic equations other than factoring?
5. Can you explain how to complete the square for solving quadratic equations?

### Tip:
When solving quadratic equations, always check if they can be factored easily. If not, other methods such as completing the square or using the quadratic formula can be very helpful.

Learn how to solve the quadratic equation x^2 - 35 with a step-by-step solution. Understand the quadratic equation formula and how to handle equations involving non-perfect square constants. Suitable for beginners.

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