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(7^3+5^2x(7^3-5^2)x-10^3=372

2 min read Jun 16, 2024
(7^3+5^2x(7^3-5^2)x-10^3=372

Solving the Equation: 7^3 + 5^2 x (7^3 - 5^2) x - 10^3 = 372

This equation may look intimidating at first glance, but with the right steps, it's easy to solve. Let's break it down:

Understanding the Equation

The equation is a combination of exponents, multiplication, and subtraction. Here's how we can simplify it:

  • Exponents: We need to calculate the powers of each number. For example, 7^3 means 7 multiplied by itself three times (7 * 7 * 7 = 343).
  • Multiplication: Next, we perform the multiplications in the order they appear.
  • Subtraction: Finally, we perform the subtraction to find the solution.

Step-by-Step Solution

  1. Calculate the exponents:

    • 7^3 = 343
    • 5^2 = 25
    • 10^3 = 1000

  2. Simplify the equation:

    • 343 + 25 * (343 - 25) x - 1000 = 372

  3. Solve the parentheses:

    • 343 + 25 * (318) x - 1000 = 372

  4. Perform the multiplication:

    • 343 + 7950x - 1000 = 372

  5. Combine like terms:

    • 7950x - 657 = 372

  6. Isolate the x term:

    • 7950x = 1029

  7. Solve for x:

    • x = 1029 / 7950
    • x ≈ 0.129

The Answer

The solution to the equation 7^3 + 5^2 x (7^3 - 5^2) x - 10^3 = 372 is x ≈ 0.129.

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