Question

The square of a number is equal to 72 more than the number. Find all such numbers.

Answer 1

You just need to think about this a little. There is a number, that you don't know, x, and if you square it (
`x^2`), that value will be equal to 72 more than the unknown number itself, so you put that into an equation.

Explanation:

`x^2=x+72\\x^2-x-72=0\\`

Apply quadratic formula (you can look it up)

`x_1=(-(-1)+√((-1)^2+(-4*1*-72) ))/(2(1)) \\\\x_2=(-(-1)-√((-1)^2+(-4*1*-72) ))/(2(1)) \\\\`

There are two answers to the quadratic formula.

The rest should be easy.