how to solve this X² - 14 = 5x and give me explation 

To solve the quadratic equation \( X^2 - 14 = 5X \), follow these steps:

1. **Rewrite the equation in standard form**:
   \[ X^2 - 14 = 5X \]
   Move all terms to one side of the equation to set it to 0:
   \[ X^2 - 5X - 14 = 0 \]

2. **Identify the coefficients**:
   \[ a = 1, \quad b = -5, \quad c = -14 \]

3. **Use the quadratic formula**:
   The quadratic formula is given by:
   \[ X = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

4. **Substitute the coefficients into the quadratic formula**:
   \[ X = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-14)}}{2(1)} \]
   Simplify inside the square root:
   \[ X = \frac{5 \pm \sqrt{25 + 56}}{2} \]
   \[ X = \frac{5 \pm \sqrt{81}}{2} \]

5. **Solve the equation**:
   Since \(\sqrt{81} = 9\), we have:
   \[ X = \frac{5 \pm 9}{2} \]

6. **Find the two possible values for X**:
   \[ X = \frac{5 + 9}{2} = \frac{14}{2} = 7 \]
   \[ X = \frac{5 - 9}{2} = \frac{-4}{2} = -2 \]

Therefore, the solutions to the equation \( X^2 - 14 = 5X \) are:
\[ X = 7 \quad \text{or} \quad X = -2 \]

### Explanation:
- **Standard Form**: We start by converting the given equation into the standard quadratic form \( ax^2 + bx + c = 0 \).
- **Quadratic Formula**: We use the quadratic formula which solves any quadratic equation by substituting the coefficients \(a\), \(b\), and \(c\).
- **Simplification**: Simplify the expression under the square root (the discriminant) and then compute the solutions using basic arithmetic.

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

### Additional Questions:
1. What is the quadratic formula, and how is it derived?
2. How do you factor quadratic equations?
3. What are the properties of quadratic equations?
4. How can you determine the nature of the roots of a quadratic equation?
5. What is the discriminant, and how does it relate to the solutions of a quadratic equation?
6. How do you solve quadratic equations by completing the square?
7. How are quadratic equations used in real-life applications?
8. What is the significance of the vertex of a quadratic function?

### Tip:
Always check your solutions by substituting them back into the original equation to verify that they satisfy the equation.

Learn how to solve the quadratic equation X² - 14 = 5x step-by-step with detailed explanations. This problem covers key algebraic concepts, including the quadratic formula and simplification of quadratic equations. Suitable for high school students and those preparing for advanced algebra.

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