To solve the quadratic equation \(x^2 - 1500x + 525000 = 0\), we can use the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \(a = 1\), \(b = -1500\), and \(c = 525000\). Plugging these values into the formula:

\[ x = \frac{-(-1500) \pm \sqrt{(-1500)^2 - 4 \cdot 1 \cdot 525000}}{2 \cdot 1} \]
\[ x = \frac{1500 \pm \sqrt{2250000 - 2100000}}{2} \]
\[ x = \frac{1500 \pm \sqrt{150000}}{2} \]
\[ x = \frac{1500 \pm 387.2983346}{2} \]

So, we get two solutions:

\[ x_1 = \frac{1500 + 387.2983346}{2} = \frac{1887.2983346}{2} = 943.6491673 \]

\[ x_2 = \frac{1500 - 387.2983346}{2} = \frac{1112.7016654}{2} = 556.3508327 \]

Therefore, the solutions to the quadratic equation \(x^2 - 1500x + 525000 = 0\) are approximately \(x_1 \approx 943.65\) and \(x_2 \approx 556.35\).

Would you like further details or have any questions about the solution process?

Here are 8 related questions to expand your understanding:

1. What are the general steps for solving a quadratic equation using the quadratic formula?
2. How do you determine the discriminant and what does it indicate about the nature of the roots?
3. Can you explain how to complete the square to solve a quadratic equation?
4. What are the applications of quadratic equations in real life?
5. How do you solve a quadratic equation graphically?
6. What is the significance of the vertex of a parabola formed by a quadratic equation?
7. How do you derive the quadratic formula?
8. What are the conditions under which a quadratic equation has only one solution?

**Tip:** When solving quadratic equations, always check the discriminant (\(b^2 - 4ac\)) first. It tells you whether the solutions are real and distinct, real and repeated, or complex.

Learn how to solve the quadratic equation x^2 - 1500x + 525000 = 0 with a step-by-step solution using the quadratic formula. Understand the algebraic process involved, including calculating the discriminant and finding approximate solutions. Suitable for high school students and those interested in algebraic problem-solving.

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