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:
- x = (5 + 13) / 2 = 18 / 2 = 9
- 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.