When 6 is subtracted from the square of a number, the result is 5 times the number. Find the positive solution.

Answer 1

Calling our unknown number "x," we get that:

x^2 - 6 = 5x

so

x^2 - 5x - 6 = 0.

This is a quadratic equation, and can be factored by finding two numbers that have a sum of -5 and product of -6. These two numbers are -6 and 1. So, x^2 - 5x - 6 = (x - 6) (x + 1) = 0.

Because this evaluates to zero, either (x-6) or (x+1) must be 0. So x is either 6 or -1, but we are looking for just a positive solution, so x = 6.

Hope this helps!