What is the positive solution of x² - 36 = 5x?

Solution:

A quadratic equation is represented as ax² + bx + c = 0 where a ≠ 0. The degree of a quadratic equation is equal to 2.

Given: x² - 36 = 5x

x² - 36 = 5x can be witten as x² - 5x - 36 = 0 in standard form.

The quadratic formula is given by

x = [-b ± √(b² - 4ac)] / 2a

We know that coefficient of x² is a, coefficient of x is b and the constant is c.

For the given equation x² - 5x - 36 = 0,

We have, a = 1, b = -5 and c = - 36

Using the quadratic formula, we get,

x = [ -(-5) ± √{(-5)²- 4 (1) (-36)}] / 2(1)

x = [5 ± √{25 + 144}] / 2

x = (5 ± √169) / 2

x = (5 ± 13) / 2

Hence, we have two solutions:

x = (5 + 13) / 2 and, x = (5 - 13) / 2

x = 18/2 and, x = -8/2

x = 9 and, x = -4

Thus, the positive solution of x² - 36 = 5x is 9.