What is the positive solution of the equation x^2 – 36 – 5x?

To solve the equation x² – 36 – 5x = 0, we can rearrange it into the standard form of a quadratic equation, which is:

x² – 5x – 36 = 0

Now, we’ll use the quadratic formula to find the solutions for x. The quadratic formula is:

x = (-b ± √(b² – 4ac)) / 2a

In this equation, a is the coefficient of x², b is the coefficient of x, and c is the constant term. Here, we have:

  • a = 1
  • b = -5
  • c = -36

Now, plug these values into the quadratic formula:

x = (5 ± √((-5)² – 4(1)(-36))) / (2(1))

This simplifies as follows:

x = (5 ± √(25 + 144)) / 2

x = (5 ± √169) / 2

x = (5 ± 13) / 2

This gives us two potential solutions:

  1. x = (5 + 13) / 2 = 18 / 2 = 9
  2. x = (5 – 13) / 2 = -8 / 2 = -4

Since the question asks for the positive solution, we select:

x = 9

Thus, the positive solution of the equation x² – 36 – 5x = 0 is 9.

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