Adding 42 to a given positive number gives the same result as squaring the number….

Explanation

Let the given positive number be x

Then x + 42 = \(x^2\)

0 = \(x^2\) - x - 42

or \(x^2\) - x - 42 = 0

\(x^2\) - 7x + 6x - 42 = 0

x(x - 7) + 6(x - 7) = 0

= (x + 6)(x - 7) = 0

x = -6 or x = 7

Hence, x = 7